IRLF 


77 


LIBRARY 


UNIVERSITY  OF  CALIFORNIA. 
Deceived ... 


ELECTRICAL 


ENGINEERING  LEAFLETS 


BY 


PROFESSOR  E.  J.  HOUSTON,  PH.  D. 

AND 

PROFESSOR  A.  E.  KENNELLY,  F.R.A.S. 


ADVANCED  GRADE 


UNIVERSITY 


1895 

THE   ELECTRICAL   ENGINEER 
NEW  YORK 


H ' 


Engineering 
Library 


^£9$, 

'UBI7BR3I.TT: 


'T'HE  Electrical  Engineering  Leaflets  have  been  pre- 
pared for  the  purpose  of  presenting,  concisely 
but  accurately,  some  of  the  fundamental  principles  of 
electrical  science,  as  employed  in  engineering  practice. 
They  have  been  arranged  under  three  grades ;  namely, 
the  Elementary,  the  Intermediate,  and  the  Advanced. 

The  Elementary  Grade  is  intended  for  those  electrical 
artisans,  linemen,  motormen,  central  station  workmen,  or 
electrical  mechanics  generally,  who  may  not  have  advanced 
sufficiently  far  in  their  studies  to  warrant  their  undertak- 
ing the  other  grades.  Here  the  mathematical  treatment 
is  limited  to  arithmetic,  and  the  principles  are  illustrated 
by  examples  taken  from  actual  practice. 

The  Intermediate  Grade  is  intended  for  students  of 
electricity  in  high  schools  and  colleges.  In  this  grade  a 
certain  knowledge  of  the  subjects  of  electricity  and  physics 
generally  is  assumed,  and  a  fuller  mathematical  treat- 
ment is  adopted.  These  leaflets,  moreover,  contain  such 
information  concerning  the  science  of  electricity,  as  should 
be  acquired  by  those  desiring  general  mental  culture. 

The  Advanced  Grade  is  designed  for  students  taking 
special  courses  in  electrical  engineering  in  colleges  or 
universities.  Here  the  treatment  is  more  condensed  and 
mathematical  than  in  the  other  grades. 

Although  the  three  grades  have  been  especially  pre- 


iv 


pared  for  the  particular  classes  of  students  referred  to, 
yet  it  is  believed  that  they  will  all  prove  of  value  to  the 
general  reading  public,  as  offering  a  ready  means  for  ac- 
quiring that  knowledge,  which  the  present  extended  use 
and  rapidly  increasing  commercial  employment  of  elec- 
tricity necessitates. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia,  March,  1895. 


CONTENTS. 


ADVANCED     GRADE. 


PAGE. 

No.  1.  ELECTRICAL  EFFECTS 1 

"     2.  ELECTROMOTIVE  FORCE 9 

"     3.  ELECTRIC  RESISTANCE 17 

"     4.  ELECTRIC  RESISTANCE 25 

"     5.  ELECTRIC  RESISTANCE 33 

"     6.  ELECTRIC  CURRENT 41 

"     7.  OHM'S  LAW 49 

"     8.  ELECTRIC  CIRCUITS 57 

"     9.  THE  VOLTAIC  CELL 65 

"  10.  THE  VOLTAIC  CELL 73 

"  11.  THE  VOLTAIC  CELL 81 

"  12.  MAGNETOMOTIVE  FORCE 89 

"  13.  MAGNETIC  RELUCTANCE.  ...    97 

"  14.  MAGNETIC  FLUX 105 

"  15.  ELECTROMAGNETS   113 

"  16.  INDUCED  E.  M.  F 121 

"  17.  THE  DYNAMO 129 

"  18.  THE  DYNAMO 137 

"  19.  THE  DYNAMO 145 

"  20.  THE  REGULATION  OF  THE  DYNAMO  . .  153 


vl 

PAGE. 

No.  21.     ELECTRODYNAMICS 161 

"     22.     THE  ELECTRIC  MOTOR,  (CONTINUOUS  CUR- 
RENT TYPE) 169 

u     23.     THE  ELECTRIC  MOTOR,  (CONTINUOUS  CUR- 
RENT TYPE) 177 

"     24.     THE  ELECTRIC  MOTOR,  (CONTINUOUS  CUR- 
RENT TYPE) 184 

"     25.     ELECTRIC  HEATING 193 

"     26.     INCANDESCENT  LIGHTING 201 

"     27.     INCANDESCENT  LIGHTING 209 

"     28.     ARC  LIGHTING 217 

"     29.     ARC  LIGHTING 225 

"     30.     ALTERNATING  CURRENTS 233 

"     31.     ALTERNATING  CURRENTS 241 

"     32.     ALTERNATING  CURRENTS 249 

"     33.     ALTERNATORS 257 

"     34.     ALTERNATORS . .  265 

"     35.     ALTERNATING  CURRENT  TRANSFORMERS.  .  273 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 
WEEKLY. 

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Electrical   Engineering  Leaflei 

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UHIVBRSITT; 


— BY— 

Prof.  E.  J.  Houston,  Ph.  D. 

.      AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED     GRADE 

ELECTRICAL 


1.  The  development  of  electrical  excitation  by 
friction,  as  is  well  known,  is  due  to  the  contact  of 
dissimilar  material  surfaces.  The  discovery  of  the  exist- 
ence of  an  electric  force  is  ascribed  to  Thales,  B.  C., 
600.  Not  only  is  the  exact  mechanism  whereby  electrical 
excitation  is  evoked  by  friction  unknown,  but  even  the 
nature  of  the  excitement  itself  yet  remains  to  be  dis- 
covered. The  electric  force  is,  however,  associated  with  a 
stress  in  an  all-pervading  medium  called  the  ether.  When 
two  dissimilar  substances  are  brought  into  contact,  a 
stress  in  the  ether  is  produced  at  the  contact  surfaces, 
and,  on  separating  the  bodies,  a  condition  of  deforma- 
tion, or  strain,  pervades  the  ether  in  the  surrounding 
space. 

Whatever  the  nature  of  the  strain  may  be,  it  is  cer- 
tainly polarized  as  regards  direction,  as  is  evident  from 
the  fact,  that  the  condition  of  excitement,  which  appears 
to  exist  at  the  surface  of  one  of  the  bodies,  is  different 

Published  by 

THE   ELECTRICAL  ENGINEER, 
203  Broadway,  New  York,  N.  Y. 

[Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  June  14,  1894.] 


from,  but  supplementary  to,  the  condition  of  excitement 
at  the  surface  of  the  other  body,  and  this  difference  or 
polarity  is  arbitrarily  referred  to  as  a  positive  and 
negative  charge  respectively. 

An  electric  charge  is  generally  supposed  to  reside  on 
the  surface  only  of  the  charged  body,  and,  so  far  as 
manifestations  of  force  are  concerned,  one  might  readily 
'believe  this  to  be  the  case,  but  it  has  been  clearly  proved 
that  the  active  disturbance  exists  in  the  medium  between 
the  two  excited  bodies,  and  that  the  so-called  charge  is 
merely  an  effect  of  the  discontinuity  of  this  strain  at 
their  surfaces. 

2.  Contact  between  dissimilar  materials  produces  an 
electromotive  force  in  the  ether  between  them,  and 
it  is  this  electromotive  force  or  stress,  which  establishes  the 
strain  in  the  ether.  The  establishment  of  such  a  strain 
is  called  an  electro  displacement  and  can  only  l)e  main- 
tained in  non-conductors  or  dielectrics.  Electric  displace- 
ment is  of  the  nature  of  a  flux^  and  follows,  in  its 
distribution,  either  the  motion  of  displacement  in  an 
incompressible  fluid  or  the  strain  in  a  compressible  iso- 
tropic  solid ;  namely,  that  as  much  flux  must  issue  from 
any  portion  of  space  as  enters  it,  provided  no  electric 
(1  large  exists  within  that  space.  This  is  only  another 
way  of  stating  the  fact  that  discontinuity  of  the  flux 
exists  at  the  surfaces  of  the  excited  bodies  or  the  boun- 
daries of  the  E.  M.  F. 

The  passage  of  a  displacement  flux  constitutes  an 
electric  current ;  a  momentary  electric  current,  therefore, 
accompanies  the  charge  and  discharge  of  a  dielectric,  and 
such  current  is  oppositely  directed  on  charge  to  what  it 
is  on  discharge.  An  electric  current  in  a  dielectric  is 


accurately  defined  as  the  time-rate  of  change  of  the  dis- 
placement, as  will  be  afterwards  more  fully  explained. 

3.  The  effects  produced  by  an  electric  discharge  or 
current  are  extremely  varied.    Among  the  most 

important  are  the  following : 

(1.)     Radiant  effects. 

(0.)     Thermal  effects. 

(3.)     Magnetic  effects. 

(4.)     Electrolytic  effects. 

(#.)     Physiological  effects. 

All  these  effects  are  believed  to  be  different 
kinds  of  motions  in  the  ether  or  in  matter.  To  the 
motion  of  the  ether  belong  the  effects  of  magnetism  and 
of  radiant  energy;  i.  e.,  heat  and  light;  while  in  the 
motion  of  the  molecules  of  matter  we  have  the  purely 
thermal  phenomena  connected  with  temperature,  and  in 
the  motions  of  the  atoms  and  radicals,  we  have  the 
phenomena  of  electrolysis. 

4.  It  is  necessary  to  distinguish  between  the  terms 
force,  work,  and  energy. 

Force  is  that  which  sets  a  body  in  motion,  arrests  its 
motion,  or  changes  the  direction  or  velocity  of  its  motion ; 
i.  <?.,  briefly  that  which  alters  the  motion  of  matter. 
Force  manifests  itself  in  a  great  variety  of  forms,  viz : 
muscular  force,  gravitational  force,  magnetic  force,  elec- 
tric force,  mechanical  force  and  the  forces  of  elasticity. 

Work  is  done  when  force  moves  matter  through  a  dis- 
tance, and  no  work  can  be  done  unless  the  force  or 
forces  applied  do  produce  such  motion. 

Energy  is  the  capability  of  doing  work  and  is  of  two 
kinds,  namely,  kinetic  and  potential.  Kinetic  energy  is 


UFI7BRSIT7 


either  the  energy  in  moving  bodies,  or  energy  actually 
doing  work ;  i.e.,  the  energy  of  motion.  Potential 
energy  is  the  energy  of  bodies  at  rest,  or  energy  not 
actually  displayed  in  motion,  but  connected  with  the 
potentiality  of  doing  work. 

5.  It  is  possible  that  potential  energy  is  only  an 
unrecognized  form  of  kinetic  energy,  just  as  the 

heat  energy  in  a  body,  which  measures  its  temperature, 
was  at  one  time  considered  to  be  potential  energy,  but  is 
now  admitted  to  be  a  form  of  molecular  kinetic  energy. 
As  knowledge  advances  it  is  probable  that  other  forms 
of  energy  now  regarded  as  potential  may  prove  in  real- 
ity to  be  due  to  motion,  either  in  matter  or  in  the  ether; 
i.e.,  kinetic  energy. 

6.  The  doctrine  of  the  conservation  of  energy  un- 
derlies all  the  phenomena  in  the  physical  sciences, 

and  the  appreciation  of  this  doctrine  underlies  all  engin- 
eering. This  doctrine  may  be  stated  as  follows  : 

The  sum  of  the  energy  in  the  whole  universe,  as 
known  to  us^  is  constant. 

When  energy  disappears  in  one  form,  an  equal  amount 
invariably  appears  in  some  other  form ;  and  force  is 
manifested  whenever  energy  changes  form  or  changes 
magnitude. 

All  natural  phenomena  are  evidences  of  energy,  and 
are  brought  about  by  forces  acting  on  matter. 

7.  For  ready  expression  and  calculation  it  is  con- 
venient to  refer  the  magnitudes  of  force,  work 

and  energy  to  certain  fundamental  scientific  units,  based 
upon  the  centimetre  as  the  unit  of  length,  the  gramme 


as  the  unit  of  mass,  and  the  second  as  the  unit  of  time. 
These  are,  therefore,  called  the  centimetre-gramme- 
second  units,  or  the  c.  G.  s.  units. 

8.       The  c.  G.  s.  unit  of  force  is  the  dyne,  and  is  that 
force  which,  after  acting  for  one  second  on  a  mass 
of  one  gramme,  imparts  to  it  a  velocity  of  one  centi- 
metre-per-second.      The  force    of   gravitation  is   com- 
monly expressed  by  the  formula, 

g  =  980.6056  —  2.5028  cos  2  I  —  0.000003  A, 


•J  ! 


5  CMS. 


AL.  WIRE  g      ^0.01  CM.  DIAM, 
SP.G. 2. 565,  AT  WASHINGTON  . .    j 
DYNAMOMETER 

FIGS.  1  AND  2. 


/ 


II 


I 
1C,*. 


— 4 — 
i 
\ 

WORK.    I  ERG. 


where  19  is  the  latitude  of  the  station,  and  A,  its  height  in 
centimetres  above  the  sea  level,  and,  consequently,  the 
weight  of  a  body  in  dynes,  i.e.,  the  force  with  which  the 
earth  attracts  the  body,  is  the  product  of  the  body's 
mass  in  grammes  and  this  force,  or 
F  —  mg 

The  dyne  is  approximately  equal  to  the  weight  of  one 
milligramme  (1.0203  mg.)  at  Washington.     (See  Fig.  1.) 

Since  the  dyne  is  often  an  inconveniently  small  unit 


of  force,  the  megadyne  (one  million  dynes)  is  frequently 
employed  in  ordinary  applications. 

The  megadyne  is  approximately  equal  to  the  earth's 
gravitational  force  on  one  kilogramme  of  matter,  i.e., 
to  the  weight  of  one  kilogramme  (1.0203  kgrn.  at 
Washington.)  A  column  of  mercury,  Y60  cms.  high,  at 
0°  C.,  which  represents  one  atmosphere,  presses  upon  its 
base  with  a  force  of  approximately  one  megadyne  per 
square  centimetre.  (1.0126  megadyne  at  Washington.) 


I- 


ACTIVITY  OR  RATE  OF  WORKING 

1  JOULE  PER  SECOND 

<=A  WATT 


1  LB.   LIFTED  0.738  FOOT— 8.84" 

PERFORMANCE  OF  1  JOULE  OF  WORK  AT  WASHINGTON 
*=10  MEGALERGS 


FIG.  3. 

1).  The  erg,  or  the  unit  of  work,  is  the  work  done 
when  the  force  of  one  dyne  acts  through  the  dis- 
tance of  one  centimetre.  (See  Fig.  2.)  The  erg  is,  there- 
fore, the  dyne-centimetre.  Since  the  erg  is  too  small  a 
unit  of  work  for  practical  purposes  (so  small  a  unit  as  one 
foot-pound,  or  the  work  done  when  a  pound  of  matter  is 
raised  through  the  vertical  distance  of  one  foot,  being 
about  13,550,000  ergs  at  Washington),  the  megerg,  or  one 
million  ergs  is  more  commonly  employed. 


One  foot  Ib.  =  13.55  mesrerffs.      )     ,  -mr    i  • 

?     „      r at  Washington, 
One  megerg  =    0.0738  foot  Ib.    ) 

It  may  be  remarked  that  the  total  amount  of  energy 
aggregated  in  the  sun  by  the  concentration  from  infinite 
diffusion  to  his  apparent  bulk  under  the  influence  of 
gravitation  would  be  2.6  X  10*s  ergs,  or  2.6  X  10*1 
joules. 

In  the  measurement  of  electrical  energy,  the  joule, 
which  is  10  megergs  (10,000,000  ergs),  is  the  unit  gener- 
ally employed. 

A  joule  is,  therefore,  =  0.738  foot  pounds  at  Wash- 
ington, or  1  foot  pound  =  1.355  joules  at  Washington. 

10.  When  work  is  done,  say,  in  lifting  a  weight 
against  gravitational  force,  the  same  amount  of 
energy  is  obviously  expended  (disregarding  air  resist- 
ance), whether  the  weight  is  lifted  in  one  minute  or  in  one 
second ;  but  in  the  latter  case  it  is  evident  that  energy  is 
expended  sixty  times  more  rapidly  than  in  the  former. 
This  rate  of  expending  energy,  or  of  doing  work,  is 
called  activity,  as  is  diagram matically  shown  in  Fig.  3. 

The  c.  G.  s.  unit  of  activity  is  the  dyne-centimetre  per 
second,  i.e.,  the  erg  per  second;  but  the  practical  unit 
usually  employed  in  engineering  is  the  watt,  which  is 
one  joule  per  second. 

The  average  activity  of  a  laborer,  working  with  pick 
and  shovel,  is  about  50  joules  per  second,  or  50  watts. 
The  average  activity  of  the  standard  horse  introduced 
by  Watt  into  engineering,  i.e.,  550  foot  pounds  per 
second  is  746  watts.  The  activity  in  a  nominal  2,000 
candle  power  arc  light  is  rated  at  450  watts  or  0,225 
watts  per  candle,  and  in  a  16  candle  power  incandescent 
lamp  is  about  50  watts  or  3J-  watts  per  candle. 


8 


For  many  engineering  purposes  the  kilowatt  (1,000 
watts)  is  the  unit  of  activity  employed.  Dynamos,  for 
example,  are  commonly  rated  in  kilowatts. 

11.  The  amount  of  energy  absorbed  by  a  machine 
is  called  its  intake.  Since  energy  is  never  de- 
stroyed, the  amount  of  work  done  by  the  machine  must 
be  rigorously  equal  to  the  intake.  Since,  however,  some 
energy  is  always  expended  in  the  machine  uselessly, 
the  useful  amount  of  work  delivered  by  the  machine, 
called  the  output,  must  always  be  less  than  the  intake. 
The  output  divided  by  the  intake  is  called  the  efficiency 
of  the  machine.  Yery  large,  well  constructed  dynamos 
of,  say,  1,000  kilowatts  capacity  have  an  efficiency  at 
full  load  of  0.96. 

SYLLABUS. 

Contact  between  dissimilar  materials  establishes  a  stress 
in  the  ether  called  electromotive  force  (E.  M.  r.) 

The  stress  produces  a  strain  flux  in  the  ether  called 
electric  displacement.  The  strain  accompanying  an  elec- 
tric charge  resides  in  the  dielectric  medium.  The  time 
rate  of  change  of  this  flux  is  an  electric  current,  flowing 
in  the  positive  direction  when  increasing,  in  the  negative 
direction  when  diminishing,  the  direction  of  the  displace- 
ment being  taken  as  positive. 

All  electrical  effects  are  believed  to  be  referable  to 
different  kinds  of  motion  either  in  the  ether  or  in  matter. 

All  energy  is  either  kinetic  or  potential.  At  any  in- 
stant the  sum  of  the  kinetic  and  potential  energies  in  the 
known  universe  is  believed  to  be  constant. 

Electrical  energy  is  conveniently  measured  in  joules. 

The  rate  of  exchange  or  development  of  energy  is 
termed  activity  and  is  measured  in  watts. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER/] 
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Electrical   Engineering   Leaflets, 


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AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED     G  F?  A  D  E  . 

ELECTROMOTIVE  KORCE 


12.  By  the  term  electromotive  force  is  meant  the 
unknown  cause  or  force  which  produces  or  tends 
to  produce  an  electric  current.  Although  but  little  is 
known  concerning  the  exact  nature  of  electromotive 
force,  (abbreviated  E.  M.  F.),  it  is  believed  to  be  associated 
with  some  variety  of  stress  in  the  ether.  This  stress 
produces  a  strain  called  displacement  which  in  the  ether 
is  permanent.  In  ordinary  matter  the  displacement 
strain  varies  according  to  whether  the  matter  is  elec- 
trically conducting  or  non-conducting.  If  conducting, 
the  strain  cannot  be  maintained ;  if  non-conducting,  it  is 
progressive,  or  advances  with  time,  like  elastic  fatigue  in 
materials  under  stress.  The  establishment  of  an  elec- 
tromotive force  is,  therefore,  invariably  attended,  in  the 
case  of  ether  or  non-conductors,  with  the  establish nient 
of  a  temporary  current,  and,  in  the  case  of  conductors  or 
a  conducting  circuit,  of  a  continued  current. 

The   entire  series  of   phenomena  accompanying  the 


Published  by 

THE   ELECTRICAL   ENGINEER, 
203  Broadway,  New  York,  N.  Y. 


10 


stress  ol  E.  M.  F.,  and  the  establishment  of  its  displace- 
ment strain,  is  called  electrification. 

13.  Although  the  exact  nature  of  a  displacement 
current  is  unknown,  yet,  quantitatively,  it  suggests 
an  analogy  to  the  following  phenomena.  Suppose,  for 
example,  that  an  electromotive  source  has  its  poles  con- 
nected respectively  with  two  elastic  conducting  globular 
or  other  surfaces  placed  in  a  homogeneous  deformable 
but  incompressible  jelly;  and,  that  under  the  influence 
of  the  E.  M.  F.,  push  and  pull  stresses  are  respectively 
exerted  on  the  jelly  at  the  surfaces  connected  with 
positive  and  negative-  poles,  producing  a  positive  pres- 
sure or  outward  thrust  at  the  positive  pole,  and  a  negative 
pressure  or  inward  thrust  at  the  negative  pole,  measured 
in  dynes  per  square  centimetre  of  surface.  Then  the 
deformations,  i.  e.  strains  or  displacements  in  the  jelly 
produced  by  the  elastic  expansion  of  the  positive  pole, 
the  elastic  contraction  of  the  negative  pole,  and  the 
yielding  of  the  jelly  between  them,  correspond  to  the 
electrical  displacements  in  the  ether  under  the  influence 
of  E.  M.  F.  The  amount  of  jelly  displaced  through  a 
bag  surrounding  either  conducting  surface  would  always 
be  the  same,  viz.,  the  increment  of  volume  of  the 
electro-positive  pole,  or  the  decrement  of  volume  of  the 
electro-negative  pole.  The  rate  of  displacement  in  the 
jelly  would  evidently  be  &flow,  just  as  the  rate  of  elec- 
trical displacement  in  the  ether  constitutes  an  electric 
current. 

The  amount  of  displacement  which  will  take  place  in 
the  jelly  for  a  given  pair  of  polar  surfaces  and  a  given 
pressure  in  them,  will  vary  with  the  distance  between 


11 


them;  so  too  the  electrical  displacement  that  will  take 
place  between  two  conducting  surfaces  at  a  given  E.  M.  r. 
varies  with  their  distance  and  disposition. 

It  should  be  remembered,  however,  that  the  preceding 
is  an  analogy  only,  and  that  the  actual  nature  of  dis- 
placement may  be  quite  different  from  what  has  just 
been  suggested. 

14.  An  electromotive  force  is  a  vector   quantity, 
that  is,  a  force  which  like  a  mechanical  force  has 

necessarily  both  direction  and  magnitude,  and,  like  a 
mechanical  force,  can  be  resolved  into  components. 

In  the  ether  or  any  non-conductor,  the  E.  M.  F.  pro- 
ducing displacement  strain  is  a  localized  vector ;  that  is, 
possesses  a  definite  magnitude  at  every  point  in  space.  In 
a  conducting  circuit,  however,  the  electromotive  force 
which  is  acting  to  send  a  current  is  equal  to  the  sum  or 
line  integral  of  all  the  E.  M.  F.'S  residing  in  the  circuit. 

In  the  International  c.  G.  s.  system  the  practical  unit 
of  E.  M.  F.  is  the  volt. 

15.  E.  M.  F.  like  all  other  forces  does  no  work  unless 
it  is  producing  motion,  i.  e.,  an  electric  current, 

and,  just  as  the  amount  of  work  done  by  a  force,  is  the 
product  of  that  force  into  the  distance  through  which  it 
moves,  or 

W=  Fd, 

so  the  work  done  by  an  E.  M.  F.  is  equal  to  the  product 
of  the  E.  M.  F.  and  the  amount  of  electric  motion  or 
quantity.  The  practical  unit  of  quantity  in  the  inter- 
national c.  G.  s.  system  is  called  the  coulomb,  and  when 
one  volt  acting  on  a  circuit  causes  one  coulomb  of  elec- 
tric quantity  to  pass  through  the  circuit,  one  joule  of 


work,  derived  from  the  electric  source,  is  expended  by 
the  E.  M.  F.  in  the  circuit. 

Generally,  therefore,  if  E,  be  the  E.  M.  F.  in  a  circuit 
(expressed  in  volts),  and  qy  the  quantity  of  electricity 
passing  through  the  circuit  (expressed  in  coulombs),  then 
the  work  done  by  the  E.  M.  F.  is 

W  =  E  q  joules; 

(  TF,  is  positive  if  ^and  q  have  the  same  sign;  and  nega- 
tive if  E  and  q  have  different  signs.  Thus  in  Fig.  4. 
the  battery  of  E  volts  sends  in  a  given  time  an  electric 


E.  M.F.  of  E  Volts 

Elec.Anyineer 

FIG.  4.  FIG.  5. 

EXPENDITURE  OF  E  q  JOULES.          EXPENDITURE  OF  E  q  JOULES. 

quantity  of  q  coulombs  through  the  conducting  circuit. 
The  equation  shows  also  that  when  W  is  negative,  the 
work  done  by  the  E.  M.  F.  is  negative,  or  work  is  done  on 
an  E.  M.  F.  when  it  opposes  a  current,  this  work  appear- 
ing in  the  electric  source  supplying  the  E.  M.  F. 

16.  This  law  is  true  both  for  conductors  and  non- 
conductors, though  in  non-conductors  no  current 
can  be  sustained.  If,  however,  an  E.  M.  F.  E,  be  in  com- 
munication with  two  conductors  insulated  from  each 
other,  such  as  two  metal  spheres,  A  and  B,  (Fig.  5.) 
separated  by  an  air  space,  an  electro-positive  or  -f-  charge 


13 


of  q  coulombs  on  a  third  electric  conductor  c,  say  a  small 
insulated  metal  globe,  between  the  two  conductors  A  arid 
B,  will,  in  effect,  be  simultaneously  attracted  by  B  and  re- 
pelled by  A.  The  total  work  which  will  be  expended  upon 
c,  in  the  passage  from  A  to  B,  under  these  forces  will  be 
W  =  E  q  joules,  as  before. 

If,  therefore,  the  quantity  in  the  movable  conductor 
c,  be  one  coulomb,  then  the  amount  of  work  in  joules  ex- 
pended in  the  transfer  from  A  to  B,  gives  in  volts  the 
E.  M.  F.,  E.  But  since  work  is  expended  continuously 
throughout  the  entire  journey,  the  work  done  in  joules 
from  departure  at  A,  to  any  intermediate  point,  measures 
in  volts  the  difference  of  potential  between  A,  and  the 
intermediate  point. 

The  difference  of  electric  potential  in  volts  between 
two  points,  is  the  energy  expended  in  joules  which  one 
coulomb  of  electricity  will  perform  in  passing  between 
the  points. 

The  sum  of  all  the  intermediate  potential  differences 
(abbreviated  P.  D.'S.)  in  the  path  of  c,  between  A  and  B,*is 
obviously  equal  to  the  E.  M.  r.  E\  and,  generally,  the 
E.  M.  F.  of  any  electric  source  at  its  poles  is  equal  to  the 
total  P.  D.  between  its  poles  in  the  external  circuit.  Any 
difference  of  potential  is  an  E.  M.  F.,  but  an  E.  M.  F.  is  not 
necessarily  accompanied  by  a  difference  of  potential. 
An  electric  current  tends  to  flow  from  a  higher  to  a  lower 
potential,  just  as  a  thermal  current  (heat)  tends  to  flow 
from  a  higher  to  a  lower  temperature. 

17.       Devices  for  producing  E.  M.  F.'S  are  called  elec- 
tric sources.     They  may  be  divided  into  classes 
according  to  the  nature  of  the  energy  they  absorb  when 
in  action,  i.  e.,  when  they  supply  a  current. 


Yoltaic  cell )  Chemical  Potential 

Charged  storage  cell f  Energy. 

(3.}  Selenium  cell )  T>  j  •     A  -n 

; .  (  mi  (  Kadiant  Energy. 

(4.)  Thermo  cell j 

(5.)  Frictional  electric  machine .  -> 

(#.)  Influence  electric  machines.  I  .... 

7  i,                    i  .  >  Mechanical  Energy. 

Magneto  machines | 

Dynamo  machines \ 

Plants  and  animals \  Vital  Energy. 

The  following  table  gives  the  E.  M.   r.   of    a 
number  of  electric  sources : 


18. 


CELL. 

PLATES. 

ELECTROLYTE. 

E.  M.  F. 

Volts. 

Bichromate         ) 
or  Grenet  \ 
Bichromate         \ 
double  fluid  f 
Bunsen             .  .  . 

1                 

zinc    carbon 

zinc    carbon 
zinc    carbon 

zinc    copper 
zinc    copper 
zinc    carbon 
zinc  platinum 
zinc    carbon 

zinc  silver  with 
chloride 

electropoin 

1.9 
2.0 
1.96 

1.072 

0.667 

2.0 
1.93 

1.47 
1.03 
2.00 

dilute  sulphuric  acid 

j  dilute  sulphuric  acid  .  .  . 
|  dilute  nitric  acid  

Daniell  

j  zinc    sulphate,     copper 

Edison-Lalande.  . 
Fuller  

dilute  caustic  soda 

j  dilute  sulphuric  acid  .  .  . 
{  bichromate  of  potash.  .  . 
j  dilute  sulphuric  acid.  .  . 

Grove  

-Leclanche.   .   . 

\  dilute  nitric  acid  

sal  ammoniac,  manganese 
dioxide 

Silver  chloride..  . 

Secondary  Cell  or 
Storage  Battery 

sal  ammoniac  

dilute  sulphuric  acid 

The  following  E.  M.  F'S  are  not  capable  of  precise  limi- 
tation.    Average  values  and  limits  are  given. 

Plating  dynamos 5  to  100  volts. 

Continuous  current  incandescent  dynamos.  50  to  150  volts. 


15 


Arc  light  dynamos 250  to  10,000  volts. 

Street  railway  dynamos 300  to  TOO  volts. 

Alternators    for    transmission   of 

power 1,000  to  4,000  volts. 


Frictional  machines 500  kilovolts  and  over. 

Influence  machines. .  . .  500  kilovolts  and  over. 


Thermo-couple .a  few  millivolts,  de- 
pending on  metals 
used  and  tempera- 
tures of  their  junc- 
tion. 


COPPER  WIRfc 


PARAFFINED  CORK 

PURE  ZINC  ROD     ' 

AIR  SPACE 


PLATINUM  WIRE  WITH 
AMALGAMATED  SURFACE 
SECTION  OF  ONE  FORM  OF 
CLARK  STANDARD  CELL 

flec.Enyineer 

FIG.  6. 


19.  The  Clark  cell  is  employed  for  accurate  com- 
parison and  measurements  of  E.  M.  r.,  and,  when 
properly  prepared,  is  considered  to  have  an  E.  M.  r.  of 
1.434  International  volts  at  15°  C.  It  is  made  up  with 
pure  mercury  and  pure  zinc  as  the  metallic  elements,  and 
pastes  of  mercurous  sulphate  and  zinc  sulphate  as  the 
electrolyte. 

A  common  form  of  such  cell  is  shown  in  FIG.  6,  in 
which  a  platinum  wire  P£,  is  sealed  into  the  glass  cell  at 
its  lower  extremity.  The  part  within  the  cell  is  first 
amalgamated  with  pure  mercury  and  is  then  surrounded 


16 


by  a  paste  consisting  of  a  mixture  of  mercurous  and  zinc 
sulphate.  The  temperature  coefficient  of  this  cell  is  usu- 
ally taken  as  0.077$  per  °C.,  so  that 

#==1.434  [1  —  0.00077  (t  —  15)]  International  volts. 
When  the  highest  accuracy  is  required  in  the  use  of  this 
cell,  certain  precautions  are  necessary  in  its  preparation, 
which  are  accurately  described  in  specifications  issued  by 
the  British  Board  of  Trade,  a  copy  of  which  is  published 
in  vol.  x,  of  the  Transactions  of  the  American  Institute 
of  Electrical  Engineers,  1893,  (page  19). 

SYLLABUS. 

.  Electromotive  force  is  the  name  given  to  the  unknown 
cause  or  force  which  produces  or  tends  to  produce  an 
electric  current. 

During  the  establishment  of  an  E.  M.  F.  displacement 
currents  are  produced. 

An  E.  M.  F.  is  a  vector  quantity,  i.  e.,  possesses  both 
direction  and  magnitude. 

An  E.  M.  F.  does  no  work  unless  it  is  producing 
motion,  i.  e.,  an  electric  current. 

E.  M.  F'S.  are  measured  in  International  volts  of  which 
a  Clark  cell  is  regarded  as  producing  1.434  at  15°  C. 

The  practical  unit  of  electric  quantity  is  called  the 
International  coulomb. 

The  transference  of  one  coulomb  through  a  difference 
of  potential  of  one  volt  is  accompanied  by  an  expendi- 
ture of  energy  of  one  joule. 

Difference  of  electric  potential  constitutes  E.  M.  F. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.! 
WEEKLY. 

3  ITT-KTV  ^O    1 k<U  Price,     -    10  Cents. 

JUNK  dO,  1  Subscription,  $3.00. 

Electrical   Engineering  Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED      GRADE. 

RLECTRIC 


20.  The  resistance  of  a  conductor  is  that  quality  in 
virtue  of  v/hich  it  limits  the  flow  of  electricity 

through  it  under  a  given  electromotive  force.  The  exact 
nature  of  resistance  is  unknown. 

The  resistance  of  a  uniform,  homogeneous  conductor 
varies  directly  as  its  length  and  inversely  as  its  cross 
sectional  area.  The  resistance  of  a  body  of  given  shape, 
depends  upon  the  nature  of  the  body. 

21.  The  practical  unit  of  electrical  resistance  is  called 
the  International  ohm,  and,  as  nearly  as  can  be 

determined,  is  equal  to  the  resistance  offered  by  a  uniform 
column  of  mercury,  14.4521  grammes  in  weight  and  106.3 
centimetres  in  length,  at  the  temperature  of  melting 
ice.  Such  a  column  would  have  a  cross-section  of  one 
square  millimetre. 

22.  Multiples  and  submultiples  of  the  ohm  are  con- 
veniently   represented    by    certain    prefixes     a& 

below. 


Published  by 

THE   ELECTRICAL  ENGINEER, 
203  Broadway,  New  York,  N.  Y. 

[Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  June  14,  1894.] 


18 


MULTIPLES.  DERIVATIVES. 

deka..  10  ten 10 

hecto..  100  one  hundred 102 

kilo...  1,000  one  thousand.    .  .10* 

mega..  1,000,000  one  million 106,  megohm. 

bega . .  1,000,000,000  one  billion 109,  begohm. 

trega..        1,000,000,000,000  one  trillion 1012,  tregohm. 

quega  1,000,000,000,000.000  one  quadrillion  .  .1016,  quegohm. 

SUB-MULTIPLES.  DERIVATIVES. 

deci 0.1  one  tenth 10-* 

centi .. .  .0.01  one  hundredth 10~2 

milli 0.001  one  thousandth 10~3 

micro . .  .0.000001  one  millionth 10~6,  microhm. 

bicro .... 0.000000001  one  billionth 10~9,  bicrohm. 

tricro.. .  0.000000000001  one  trillionth 10-1 3,  tricrohm. 

The  fundamental  c.  G.  s.  unit  of  resistance  is  a  Mcrohm, 
and  its  value  is  such  that  one  c.  G.  s.  unit  of  current 
passing  through  it,  expends  an  amount  ^  of  energy  equal 
to  one  erg  each  second. 

23.  By  the  resistivity  or  specific  resistance  of  a  body, 
is  understood  the  resistance  of  a  cubic  centimetre  of 
the  body,  measured  between  opposite  faces,  at  the  tem- 
perature of  zero  centigrade.  The  following  is  a  table  of 
the  resistivities  of  various  common  substances  expressed 
in  International  ohms.  Thus  the  resistivity  of  pure,  soft 
or  annealed  copper,  the  metal  most  frequently  used  in 
electrical  instruments,  is  1.594  microhms  at  0°  C.,  and 
increases,  as  shown  by  the  temperature  coefficient  in  the 
third  column,  according  to  Matthiessen,  0.388  per  cent, 
per  degree  centigrade  for  a  small  variation  of  tempera- 
ture. An  inspection  of  the  table  will  show  that  while 
the  resistivity  of  almost  all  the  pure  metals  is  markedly 
different,  yet  the  temperature-coefficient  for  the  small 


limits,  already  mentioned,  is  practically  the  same  with 
the  exception  of  liquid  mercury.  The  temperature- 
coefficients  of  the  alloys,  however,  is  much  less  than  that 
of  the  ingredient  metals.  The  resistivity  of  carbon 
(graphite)  is  about  0.07  ohm,  and  its  temperature- 
coefficient  is  negative,  that  is  to  say,  the  resistance  dimi- 
nishes with  the  temperature.  For  example,  in  the 
incandescent  electric  lamp,  the  resistance  of  the  carbon 
filament  when  cold,  is  about  twice  as  great  as  at  the  in- 
candescent working  temperature. 


Substance. 

Tempera- 
ture. 

Resistivity. 

Tem- 
perature 
Coeffi- 
cient. 

Authority. 

Silver,  annealed  .  . 
Silver,  hard  drawn 
Copper,     annealed 
(M  a  1  1  h  i  e  s  en's 
standard)  

0° 

< 
t 

c. 

( 

l.SOOmicr 
1.53 

1.594 
1.629 
2.052 
2.089 

2.903 
5.598 
9.030 
9.687 
12.420 
13.17 
19.57 
35.40 
130.8 
94.84 

2432       ' 

ab't20.9  ' 
"    32.7  < 

"    68.0  ' 

ohms 

i 
i 

0.377 
it 

0.388 
t» 

0.365 
6.365 

6.'365 
0387 
0.389 
0.354 
0.072 

0.031 
0.044 
0.021 

0.1.22 

Ma.tth 
Flemi 

lessen. 
Dg, 

Copper,  hard  dr'wn 
Gold,  annealed...  . 
Gold,  hard  drawn.. 
Aluminum,        an- 
nealed   .  . 

Zinc,  pressed  

Platinum,  annealed 
Iron,  annealed.  .  .  . 
Nickel,  annealed  .  . 
Tin,  pressed 

Lead,  pressed  
Antimony,  pressed. 
Bismuth,  pressed  .. 
Mercury,  liquid  .  . 
Platinum-silver  al- 
loy, 2  parts  Pt. 
to  one  Ag.  hard 
or  annealed  
German  silver  ... 
Platinoid  

Hadfield's       man- 
ganese steel.     . 

Substance. 

Tempera- 
ture. 

Resistivity. 

Tem- 
perature 
Coeffi- 
cient. 

Authority. 

Selenium  
Retort  carbon  

Graphite  

0°C. 

"     \ 

ab't  59000ohms 
"    0.07      " 
from  0.0024  to 

1.0 

[  about 
C—  0.5 

Mattheissen. 
j-  Everett. 

Ice 

} 
—  124° 

0.042  ohms 
2  24  begohms 

....-j 

Ayrton  & 

Ice             

—    0.2 

0284 

Perry. 

Sulphate    of     zinc 
saturated     solu- 
tion              

10° 

33  6  ohms 

Bwing  & 
Macsrrefiror 

Sulphate  of  zinc  .  . 
Common  salt 

10° 

28.22    "  1       >> 
47"         '"> 

"  \ 

«i 

Kohlrausch 

Sal  ammoniac  
Sulphate  of  soda.  . 
Sulphuric  acid   in 
water  • 

« 

'  '             «g  •-£ 
2.5      «      S-S 
11.3     "     |  £ 

i  376  "      ^5 

"  ( 

&  Nippoldt. 

Nitric  acid  in  water 
Hydrochloric   acid 
in  water  

tt 

1.287"      oSJ 
1  316      j       ~ 



<  < 

Pure  water 

,    \ 

about  3.75  meg- 

I 

Kohlrausch 

Sample,  of  hydrant 
water  

I 
15°  C.  \ 

ohms 
about  200,000 

r; 
[ 

Kennelly. 

Mica  
Gutta-percha. 

1 
20° 

24° 

ohms 
84  tregohms.  . 

449        " 

f 
j 

Ayrton  & 
"Perry. 
Latirner 

Shellac. 

28° 

9  Quegohms 

'"( 

Clark. 
Ayrton  & 

Hard  rubber     .... 
Paraffin 

46° 
46° 

28 
34        " 

""\ 

Perry. 

Glass   flint  . 

0° 

16700    " 

Foussereau 

Porcelain  

0° 

540        " 

a 

Commercial  stearic 
acid, 
olive  oil 

15° 

440  tregohms 

— 

Kennelly. 

"        lard  oil. 

350  begohms  .  . 

C 

"         creosote 
"        benzine. 
"        benzole. 

5.4  megohms 
14  tregohms 
1.3  begohms. 

i 

t 

21 


The  resistivity  of  pure  water  has  been  observed  by 
Kohlrausch  to  be  3.75  megohms,  and  since  an  exceed- 


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III  I  I 

FIG.  7. — DIAGRAM  OF  RESISTIVITIES  AT  DIFFERENT  TEMPERATURES, 
(DEWAR  AND  FLEMING.) 

ingly  small  trace  of  impurities  greatly  decreases  its  re- 
sistance,   it   is    probable    that    Kohlrausch's    value    is 


much  below  the  resistivity  of  pure  water,  which  in 
the  opinion  of  some  would  be  almost  infinite.  The 
temperature-coefficient  of  all  liquids  is  negative.  The 
temperature-coefficient  of  all  insulators  is  also  negative. 

In  order  to  point  out  more  clearly  the  relation  of  re- 
sistance to  temperature  in  different  substances,  the  dia- 
gram Fig.  7,  gives  a  series  of  curves  of  observed 
resistivities  for  different  substances  at  various  tempera- 
tures. 

Various  formulae  have  been  advanced  at  different 
times  for  reducing  the  resistance  or  resistivity  of  a  metal 
at  one  temperature  to  its  corresponding  value  at  another, 
but  this  temperature,  variation*  appears  to  differ  appreci- 
ably with  different  samples  of  even  the  purest  metals, 
or,  at  least,  the  experimental  results  are  not  yet  in  suffi- 
ciently close  accordance  to  make  any  formula  reliable. 
The  most  convenient  supposition  is,  that  the  variations  in 
resistance  are  proportional  to  the  variations  in  tempera- 
ture which  produce  them,  or  that  the  curves  in  Fig.  7 
are  straight  lines.  Some  of  them  do  in  fact  appear 
from  the  observations  to  be  sensibly  straight  lines.  On 
this  supposition 

Pt  =  Po  (1  +  «  0 

where  pt  is  the  resistivity  at  any  temperature  t°  C.,  p0 
the  resistivity  at  zero  centigrade,  and  a  is  an  experiment- 
ally determined  constant. 

From  the  measurements  of  Dewar  and  Fleming  as  re- 
presented in  Fig.  7,  the  mean  value  of  the  constant  «, 
between  0°  and  100°  C.  is,  for 

Platinum 0.00358 

Gold  .  .  .0.00376 


23 


Silver  .......................  0.0040 

Copper  .......................  0.00422 

Aluminum  .............  .....  ..0.00475 

Nickel  ......................  0.00548 

Iron  ..........................  0.00655 

Carbon  .......................  0.00391 

Platinum  Silver  ................  0.000224 

Platinoid  ....................  0.000253 

German  Silver  ......  .  .........  0.000317 

According  to  Matthiessen's  observations  which  have 
hitherto  been  generally  accepted,  the  formula  of  correc- 
tion for  pure  copper  to  any  temperature  between  0°  and 
100°  C.  is  approximately.  • 
/>t  =  14-0.00387(H  +  5.968xlO-6  ts—  1.177X10-8  t*—  9.93  X  10-11*4. 

The   resistance  of  any  homogeneous  conductor  may, 
therefore,  be  calculated  by  the  following  formula  — 


where  I    —  the  length  of  the  conductor  in  centimetres. 
a  —  its  cross-section  in  square  centimetres. 
pt  —  the  resistass&y  at  the  observed  temperature 


. 

Thus   the   resisfc&^L  of  a   mile   of    copper   wire   of 

Matthiessen's   standard,    1  sq.    mm.  in    cross-section   at 
0°  C.  is 

1  f\C\  Q^'-i 

—     Q  ^      X  1.594  microhms  =  25,652,720  microhms 
or  25.65  ohms  approximately. 


SYLLABUS. 

The  resistance  of  a  uniform  homogeneous  conductor 
varies  directly  with  its  length  and  inversely  with  its  area 
of  cross-section. 

The  International  ohm  is  the  practical  unit  of  electric 
resistance. 

In  order  to  conveniently  designate  the  decimals,  mul- 
tiples and  submultiples  of  a  quantity,  suitable  prefixes 

are  employed. 
ICT" 

The  bj&^ohm  is  the  fundamental  c.  G.  s.  unit  of  re- 
sistance. 

The  resistivity  of  a  homogeneous  isotropic  body  is  the 
resistance  of  a  column  of  that  body,  having  unit  length 
and  cross-section. 

The  resistivity  of  all  metals  increases  with  tempera- 
ture. 

The  resistivity  of  carbon,  selenium,  liquids  and  solu- 
tions, as  well  as  insulators  diminishes  with  temperature. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia.         « 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.! 

WEEKLY. 
i 

4.  TITTV  7    1KQ4-  Price>     '    10  Cellts> 

JUIA  7,  1  Subscription,  $3.00. 

Electrical   Engineering   Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.,R.  A.  S. 


ADVANCED     GlfcADE. 

ELECTRIC 


24.  Conductivity  is  the  reciprocal  of  resistivity,  and 
conductance  the  reciprocal  of  resistance.  Thus  the 
minimum  resistivity  of  an  aqueous  solution  of  nitric  acid 
being  1.287  ohms,  the  maximum  conductivity  is  T.^T  — 
0.777  mho,  the  mho  (ohm  spelled  backwards)  being  the 
unit  of  electrical  conductance.  A  wire  which  has  two 
ohms  resistance  has  0.5  mho  conductance. 

The  total  resistance  of  a  number  of  separate  resist- 
ances, connected  in  series,  is  equal  to  their  sum,  and  the 
total  conductance  of  a  number  of  separate  conductances, 
connected  in  parallel,  is  equal  to  their  sum. 

Thus,  if  a  number  of  resistances  of  #,  &,  <?,  ...  n, 
ohms,  respectively,  be  connected  in  parallel,  their  respec- 
tive conductances  will  be  -»  75  -  •  •  — .  Their  total  con- 

a  o  c  n 

ductance  will  be  ( -  -|-  v  -(---)-....+  -)  and  their 

\  Cu  (J  Q'  / 


total  resistance  i  "  i    * 
a        T) 


Published  by 

THE   ELECTRICAL  ENGINEER, 
203  Broadway,  New  York,  N.  Y. 

[Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  June  14,  1894.] 


Thus,  if  three  resistances  be  connected  in  parallel  of 
20,  50,  and  80  ohms  respectively,  their  respective  con- 
ductances will  be  0.05,  0.02,  and  0.0125  mho.  Their 
joint  conductance  will  be  0.0825  mho,  and  their  joint 
resistance  12.12  ohms. 

25.  The  resistance  of  any  metallic  wire  increases 
with  its  temperature.    Where  a  constant  standard 

resistance  is  required,  this  is  an  objectionable  feature. 
Since  the  effect  of  temperature  is  less  marked  on  alloys 
than  on  their  ingredients,  alloys  are  generally  used  for 
standard  resistances. 

The  alloys  most  frequently  used  for  this  purpose  are 
platinum-silver,  german-silver,  manganin,  and  platinoid, 
or  (german-silver  with  one  or  two  per  cent,  of  tungsten.) 

The  resistance  of  some  alloys  is,  however,  owing  to  a 
tendency  to  crystallize,  apt  to  be  subject  to  slight  vari- 
ations with  time.  Platinum-silver  or  platinoid  appear 
to  be  the  two  alloys  most  nearly  free  from  this  objection, 
and  are,  therefore,  most  frequently  employed  in  the  con- 
struction of  standard  resistance  coils. 

26.  All  gases  at  ordinary  temperatures  and  pressures 
have  such  high  resistivities  that  these  have  never 

yet  been  measured.  When,  however,  the  pressure  is 
greatly  reduced,  the  resistivity  becomes  very  low,  and  in 
certain  recent  experiments  with  air  at  a  pressure  of  0.01 
min.  mercury,  or  about  13  dynes  per  sq.  cm.,  the  resistivity 
of  the  air  was  apparently  about  1.4  ohms. 

27.  Resistances  may  be  measured  in  various  ways 
which  may  be  conveniently  divided  into  classes 

according  to  the  magnitude  of  the  resistances  and  the 
degree  of  accuracy  required. 


27 


(1.)  Very  high  resistances  (upwards  of  one  begohm) 
by  electrometer  methods,  in  which  the  rate  of  loss  of 
charge  by  leakage  is  observed. 

(#.)  Resistances  from  one  megohm  to  one  begohm,  by 
galvanometer  deflection,  where  a  deflection  through  a 
known  resistance  serves  to  vain  ate  the  unknown  resist- 
ance. 

(3.)  From  Ti7  ohm  to  one  megohm,  by  a  differential 
galvanometer  or  a  Wheatstone  balance. 

(4.)  Below  y^-Q  ohm,  by  potentiometer  measurements. 

28.       The  method  most  frequently  employed  for  the 
usual  range  of  resistances  is  the  Wheatstone  bridge 
or  balance,  a  form  of  which  is  represented  in  Fig.  8. 


Elec-Engineer 


FIG.  8. — DIAGRAM  OF  WHEATSTONE  BRIDGE. 
In  this  method,  as  is  well  known,  an  unknown  re- 
sistance  is    measured    in    terms    of    a    known    resist- 
ance by  so  proportioning  the  resistances  A,  B  and   C 
that  no  current  flows  through  a  galvanometer,  represented 

by  the  resistance  G-,  connected  to  the  circuit  as  shown. 

£ 
When  balance  is  obtained  X  =  O  -&.  When  the  arms  A, 

and  B,  are  equal,  X  =  C  and  the  unknown  resistance  is 
equal  to  the  resistance  in  the  bridge.  In  practiced,  and 
B,  are  some  multiple  of  10  ohms  between  10  and  10,000 


and  the  resistance  (7,  can  be  adjusted  by  single  ohms  be- 

A 
tween  0  and  10,000,  so  that  making  the  ratio  -    = 


Klec.Engi 


YIG.  9.— VARIOUS  FORMS  OF  RESISTANCES. 

or  i\\°-2-,  the  total  range  of    the   instrument  is  from 
__i_th  ohm  to  10  megohms. 

The  best  resistance  to  employ  in  A  and  Z?,  depends 


upon  the  resistance  of  the  galvanometer  and  that  of  the 
unknown  resistance.  Where  these  are  small  A  and  B, 
should  be  comparatively  small ;  where  they  are  large  A 
and  B,  should  be  large. 

Fig.  9  represents  various  forms  of  resistances,  a,  is  a 
compact  form  of  bridge  with  keys  to  close  the  battery 
and  galvanometer  circuits.  5,  is  a  slide  form  of  meter 
bridge  in  which  the  arms  A  and  B,  (in  Fig.  8)  are  altered 
simultaneously  by  the  shifting  of  a  contact  along  the 
wire.  Such  a  form  is  only  used  for  the  measurement  of 
low  resistances,  say  under  20  ohms,  c,  is  a  form  of  dial 
bridge  with  keys  attached,  d,  and  6,  are  more  elaborate 
forms  of  dial  bridges.  The  dial  pattern,  though  some- 
times more  expensive  than  the  ordinary  box  type  of 
Wheatstone  bridge,  has  the  advantage  that  there  is  less 
chance  of  additional  resistance  being  introduced  by  bad 
contacts,  only  four  or  five  plugs  being  used,  so  that  the 
danger  of  additional  resistance  by  loose  contacts  is 
largely  avoided.  At/",  is  shown  a  form  of  megohm,  in 
wire,  carefully  insulated  and  divided  into  ten  coils  of 
100,000  ohms  each. 

At  </,  is  represented  a  form  of  megohm  in  carbon 
(pencil  mark)  on  ground  glass.  This  form  of  resistance 
is  not  reliable  for  accurate  measurements  and  is  only 
used  for  approximate  work. 

30.  It  is  evident  that  the  accuracy  of  measurement, 
by  whatever  method  that  may  be  employed,  de- 
pends upon  the  accuracy  of  the  standard  resistances  of 
comparison.  It  has  been  found  in  practice  most  conveni- 
ent to  make  this  fundamental  standard  of  the  value  of  an 
ohm.  Three  forms  of  standard  ohms  are  shown  in  Fig. 
10.  At  x  is  shown  the  form  in  common  use.  More 


30 


modern  forms  are  shown  at  Y  and  z.  In  all  cases  the 
difficulty  of  employing  the  instrument  is  in  determining 
the  true  temperature  of  the  coil  of  wire,  the  temper- 
ature being  inferred  from  that  of  a  mass  of  water  or  oil 
surrounding  the  coil.  The  improvements  in  Y  and  z, 
Fig.  10,  consist  in  exposing  a  large  surface  of  the  liquid 
and  providing  means  for  stirring  the  same  in  order  to 
rapidly  equalize  the  temperature  within  and  without. 

The  standard  megohms  are  employed  for  the  purpose 
of  calibrating  galvanometers. 


FIG.  10. — FORMS  OF  STANDARD  RESISTANCES. 

31.  The  materials  of  which  the  earth's  crust  is  formed 
have  an  exceedingly  high  resistivity  when  wholly 
dry  and  may  almost  be  classed  as  insulators,  so  that  the 
resistance  of  the  earth's  crust  as  a  whole,  if  perfectly 
dry,  may  be  very  great.  In  nearly  all  regions,  however, 
the  surface  strata  are  permanently  moist,  and,  since  such 
moisture  contains  various  saline  matters  in  solution,  the 
resistivity  of  the  ground  is  usually  less  than  100  ohms. 


31 


Therefore,  the  ground  may  be  used  in  place  of  a  second 
conductor  to  complete  a  circuit  between  two  stations. 

32.  It  may  be  supposed  that  like  all  conductors  the 
resistance  of  the  ground  as  measured  between 
two  ground  plates  would  increase  in  proportion  to  the 
distance  between  them.  In  the  case,  however,  of  a  large 
conducting  mass  such  as  that  of  the  earth  it  can  be 
shown  that  such  is  not  the  case,  for  the  following  reason. 
If  two  metallic  hemispheres  A  and  B  (Fig.  11)  be  buried, 
as  shown,  in  the  surface  of  a  conducting  medium,  in- 
finitely extended  below  the  infinite  horizontal  plane  c  A 
B  D,  the  resistance  as  measured  between  A  and  B,  will  be 


Elec.Engineer 

FIG.  11. 


where  />,  is  the  resistivity  of  the  medium  in  ohms  ; 
-  =  3.1416,  /•',  is  the  radius  of  each  hemisphere  in  centi- 
metres ;  and  d,  is  the  distance  between  the  centres  of  the 
hemispheres  in  centimetres. 

From  which  it  is  evident  that  the  distance  between 
the  hemispheres  does  not  appreciably  aifect  the  value  of 
the  .resistance  7?,  which  may  be  taken  as 

i  +  i 


or,  when  the  hemispheres  have  equal  radius, 


32 


TT  r  '   ,^: 

Thus  if  />,  the  resistivity  of  the  medium  =  100  ohms, 
and  r,  the  radius  of  the  hemispheres  is  1  metre,  the  re- 
sistance of  the  ground  =  0.318  ohm. 

The  distance  r/,  fails  to  appreciably  affect  the  resistance 
72,  owing  to  the  fact  that  the  current  is  by  no  means 
confined  to  the  portions  of  the  medium  lying  directly 
between  A  and  B,  but  diffuses  or  spreads  through  the 
entire  mass  of  the  infinitely  extended  medium. 

SYLLABUS. 

Very  large  resistances  are  usually  measured  by  electro- 
meters or  galvanometer  deflections. 

Yery  small  resistances  are  usually  measured  by  poten- 
tiometers. 

Intermediate  resistances  are  usually  measured  by  means 
of  the  Wheatstone  bridge  by  properly  proportioning  the 
resistance  in  the  bridge  arms.  The  Wheatstone  bridge, 
as  ordinarily  constructed,  may  measure  resistances  from 
TJj-0th  ohm  to  one  megohm  and  is  frequently  constructed 
for  TTi0_0-th  ohm  to  10  megohms. 

In  order  accurately  to  determine  the  resistance  of  a 
standard  coil  its  true  temperature  requires  to  be  known. 

The  resistivity  of  nearly  all  the  materials  forming  the 
earth's  crust  is  high.  The  presence  of  water,  however, 
renders  the  resistivity  of  the  mass  much  lower.  The 
resistance  of  a  ground  return  in  a  circuit  may,  therefore, 
be  only  a  fraction  of  an  ohm. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 
WEEKLY. 

^  TTTTV  14-    1 8Q4.  Price,     -    10  Cents. 

JUIA  14,  1  Subscription,  $3.00. 

Electrical    Engineering   Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED     GRADE. 

ELECTRIC 


33.  If    the  resistivity  of    the  insulating  materials 
alone   had   to  be  considered  their  specifications 

would  offer  but  little  choice.  In  actual  practice  the  re- 
sistance of  an  insulator  is  determined  not  so  much  by 
its  dimensions  and  resistivity,  as  by  the  leakage  afforded 
through  the  film  of  dust  and  moisture  which  collects  on 
its  surface.  For  this  reason  the  best  form  of  insulation 
is  that  which  affords  the  longest  and  narrowest  path  for 
leakage.  In  cases  where  very  high  insulation  is  desired, 
some  form  of  oil  insulator  is  employed,  the  principle 
being  to  insert  in  the  circuit  of  the  leakage  path  a  film 
of  oil  whose  resistivity  is  not  only  great,  but  which  is 
automatically  kept  clean  by  the  tendency  of  dust  to 
settle  and  fall  to  the  bottom.  (See  Fig.  12.) 

34.  The  insulation  resistance  of  a  line  or  conductor 
is  measured  in  megohms,  and  this  total  insulation 

multiplied  by  the  length  of  the  line  in  miles,  gives  the 
average  apparent  insulation  per  mile  in  megohm-miles. 

Published  by 

THE  ELECTRICAL  ENGINEER, 
203  Broadway,  New  York,  N.  Y. 

[Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  June  14,  1894.] 


On  the  other  hand,  the  metallic  resistance  of  a  conduc- 
tor divided  by  its  length  gives  its  apparent  conductor  re- 
sistance per  mile.  On  long  lines  the  effect  of  the  escape 
of  the  measuring  current  by  leakage  will  be  to  make  the 
apparent  insulation  per  mile,  -7?appt  too  high,  and  the  ap- 
parent conductor  resistance  per  mile,  7iapp(  too  low.  These 
values,  corrected  for  leakage  through  uniform  insulation, 
are : 


r  =    y  J?app.  /vPp.  tanh-1 


^app. 


'^app. 
^?ann 


app, 


FIG.  12.—  OIL  INSULATOR. 

For  example  :  If  the  apparent  insulation  R^v.  °^  a 
uniform  line  200  miles  long,  was  6024  ohms,  and  when 
grounded  at  the  distant  end  its  apparent  conductor  resis- 
tance was  2656  ohms,  then  the  corrected  conductor 


resistance  =    |/6024  X  2656  tanh-1  V  f|S?  =  4000  X 

6024 

0.8  =  3200  ;  that  is,  16  ohms  per  mile  •  and  its  corrected 

.     /Ofv^l-t 

V   ~  = 


_ 

insulation  R  =  </6024  X  2656 


4000 


35 


X  1.25  =  5000  ohms;  that  is,  1  megohm  mile.  The 
apparent  values  would  be  13.28  ohms  per  mile  and 
1.2048  megohm  miles.  But  6024  X  2656  =  5000  X 
3200  =  16,000,000,  and  in  all  cases  where  leakage 
through  uniform  insulation  resistance  has  the  effect  of 
diminishing  the  conductor  resistance  by  any  ratio,  the 
insulation  resistance  apparently  increases  in  the  same 
ratio,  so  that  the  product  of  insulation  resistance  and 
conductor  resistance  remains  constant. 

35.  The  best  resistance  to  give  to  the  coils  of  any 
electromagnetic  relay  or  other  receptive  device 
operated  at  the  receiving  end  in  a  ground  return  cir- 
cuit, is  the  resistance  which  the  circuit  offers  from  the 
receiving  end.  This  resistance,  owing  to  the  influence 
of  leakage,  may  be  considerably  less  than  the  conductor 
resistance  of  the  line.  This  rule  applies,  strictly  speak- 
ing, to  a  very  slow  rate  of  signalling  in  telegraphy,  and 
for  rapid  signalling  the  resistance  of  the  relay  should 
be  much  lower. 

35A.  We  have  seen  that  the  resistance  of  a  conductor 
depends  upon  its  resistivity  and  its  geometrical 
form.  When  the  form  is  simple,  as  in  the  case  of  wires, 
the  computation  of  the  resistance  offers  no  difficulty. 
When,  however,  the  form  is  more  complex  a  difficulty 
arises,  for  example,  in  determining  the  insulation  resist- 
ance of  a  uniform  cable  consisting  of  a  conducting  wire 
and  concentric  external  sheath,  the  insulator  having 
known  resistivity  and  known  dimensions.  In  this  case 
the  resistance  per  centimetre  would  be  expressed  by  the 
formula, 


36 


where  0,  equals  the  resistivity  (ohms.) 
1),  equals  the  external  diameter. 
<f,  equals  the  internal  diameter. 
s,  equals  the  ISTaperian  base. 

That  is,  if  p  =  300  begohms,  D  =  1  inch,  d  =  0.5 

inch,  then ;  ^  =  2,  log  ~  =  0.30103  ; 
cl>  cL 

R  =  0.3665  X  300  X  109  X  0.30103 ;  =  33.1  beg- 
ohms per  centimetre ;  this  divided  by  160,933,  the  num- 
ber of  centimetres  in  a  mile,  gives  0.2057  megohms  to 
the  mile,  i.  e.,  0.2057  megohm-mile. 

36.  A  common   error  in  less  recent  text-books  is 
found  in  the  belief  that  electric  resistance  par- 
takes of  the  nature  of  a  velocity.     This,  however,  while 
true   for   the   existing   system  of   electrical  dimensions 
in  the  electromagnetic  system,  where  resistance  appears 
as  a  length  divided  by  a  time,  is  only  a  misconception  de- 
rived from  incomplete  knowledge.     The  real  nature  of 
resistance  is  yet  unknown. 

37.  When  a  galvanometer  in  a  circuit  gives  too  high 
a  deflection,  it  is  usual  to  reduce  this  deflection 

by  the  introduction  of  a  bypath  or  shunt.  For  ex- 
ample, when  the  galvanometer  of  resistance  6r,  has  its 
terminals  connected  by  the  shunt  S9  its  deflection  will 

O  fl     I      o 

be  reduced  by  the  factor  — ^,  whose  reciprocal,  — 3l — 

6r  +  £  XS 

is  called  the  multiplying  power  of  a  shunt.  To  obtain, 
therefore,  a  shunt  with  a  multiplying  power  of  1000  for  a 

KAAA       |         & 

galvanometer  of  5000  ohms  resistance,  we  have ' 

o 

=  1000,  so  that  8  —  $gg$-  or  -^th  part  of   the  galva- 


37 


nometer's  resistance,  and  generally  the  resistance  of  a 
shunt  must  be  (n  —  1)  times  less  than  the  resistance  of 
the  galvanometer  in  order  to  have  the  multiplying, 
power  of  n. 

38.  In  the  use  of  any  high  resistance  apparatus  it 
is  absolutely  necessary  that  the  insulation  of  the 
apparatus  be  as  high  as  possible,  for  the  effect  of  leak- 
age may  be  to  considerably  reduce  the  resistance  of  the 
apparatus  as  computed.  For  example,  a  box  containing 
one  megohm  in  resistance  might  easily  have  a  leakage 
resistance  over  the  surface  of  the  box  between  the  ter- 
minals of  one  begohm.  The  effect  of  this  very  small 
leakage  would  be  to  shunt  the  megohm  by  a  resistance  one 
thousand  times  as  great,  and  the  effect  would  be  to  re- 
duce the  resistance  of  the  box  by  about  1000  ohms,  and 
leave  the  apparent  total  of  999,000  ohms  approximately. 

In  practice  the  problem  frequently  presents  itself  of 
determining  the  size  of  wire  required  to  fill  a  spool  or 
bobbin  of  certain  dimensions.  To  do  this  we  first  cal- 
culate the  volume  of  space  required  to  be  filled  by  the 
wire,  and  then  employ  the  following  formula : 

d  =  —  t  +  V  #  4-  0.0009432  V—  ; 

r 

where  d  =  diameter  of  the  wire  in  inches 

t  =  thickness  of   insulation   (inches).     If  D  be 

the  covered  diameter,  2  t  =  J)  —  d. 
v  =  volume  of  winding  space  in  cubic  inches 
r  =  the  resistance  required  in  the  winding  (ohms) 

The  resistivity  of  the  wire  is  here  assumed  to  be  1.775 
X  10"6  (copper  of  0.97  Matthiessen's  conductivity  at 


38 


In  practice  t  has  the  following  values : 

Silk,       single   covering,  0.0005  to  0.001  inch. 
Silk,       double  covering,  0.0015  to  0.002  inch. 
Cotton,  single   covering,  0.0035  to  0.004  inch. 
Cotton,  double  covering,  0.005    to  0.007  inch. 
The  precise  thickness  of  the  coat  depends  upon  the 
size  of   the  wire.      Large  wires   usually   take   heavier 
thicknesses  of  insulator. 

Thus  a  spool  of  two  inches  intern1  ange,  i.  e.,  length 
between  flanges,  h&s  an  internal  or  core  diameter  of  0.5 
inch,  and  an  external  diameter  when  fully  wound  of  1.0 
inch.     The  resistance  of  the  winding  is  to  be  20  ohms, 
with  a  double  silk  covered  copper  wire,  in  which  the 
insulation  increases  the  diameter  of  the  wire  by  three 
mils.     Find  the  required  diameter. 
Here  t  =  0.0015;^  =  2  X  0.5891  =  1.1 782  cubic  inches; 
r  —  20,  v/r  =  0.05891   \fvjr  =  0.2427. 
d  =  —  0.0015  +   1/0.0000023  +  0.0002289 

-  0.0015  +  0.0152  =  0.0137  inch. 
The  nearest  size  to  this  is  No.  27.  B.  &  S.,  0.0142 
inch,  which,  when  covered  with  the  required  thickness 
of  silk  has  a  diameter  of  0.0172  inch.  There  would  be 
15  layers  of  this  wire,  each  layer  having  11(3  turns, 
supposing  the  winding  perfectly  regular  and  complete. 
The  total  number  of  turns  would,  therefore,  be  1740; 
and  the  mean  turn  length  being  2.356  inch  the  total 
length  of  wire  =  341.6  feet.  =18  ohms.  The  resistance 
is  two  ohms  less  than  that  required,  owing  to  the  differ- 
ence between  the  diameter  of  the  wire  that  has  to  be 
selected  and  the  calculated  diameter. 

When  the  thickness  of  insulation  is  very  small,  the 
formula  becomes  approximately 


39 


d  =  —  t  +  0.03071 

r 
Thus,  taking  the  above  case, 

V  -  =  0.4926, 

T 

and  d  =  —  0.0015  +  0.0151 

=  0.0136  inch. 

39.  When  plates  of  pure  amalgamated  zinc  are  im- 
mersed in  an  aqueous  solution*  of  pure  zinc  sul- 
phate it  has  been  observed  that  no  appreciable  resistance 
exists  in  the  surface  of  contact  between  the  two.  If, 
therefore,  the  resistivity  of  zinc  and  the  resistivity  of  the 
solution  were  known,  the  resistance  of  the  combination 
could  be  determined.'  Generally,  however,  such  contact 
surfaces  between  metals  and  liquids  appear  to  possess  a 
small  definite  resistance,  called  surface-contact  resistance, 
in  addition  to  the  electromotive  force  which  is  usually 
established  there. 

SYLLABUS. 

The  insulation  resistance  of  a  line  or  conductor  is 
usually  measured  in  megohms  and  its  apparent  insulation 
per  mile  in  megohm-miles. 

The  apparent  conductor  resistance  of  a  line  divided  by 
its  length  in  miles  gives  the  apparent  conductor  re- 
sistance per  mile. 

An  electromagnetic  relay  or  other  receptive  device  at 
the  receiving  end  of  a  ground  return  circuit  should  with 
a  slow  rate  of  signalling,  preferably  have  a  resistance 
equal  to  the  resistance  which  the  circuit  offers  from  the 
receiving  end. 

The  resistance  of   a  conductor  depends  upon  its  re- 


V  °'ra*      ^ 

fUiriVERSITT; 


sistivity,  on  its  geometrical  form,  but  in  all  except  very 
simple  forms  the  computation  becomes  complex. 

It  is  a  mistake  to  believe  that  the  nature  of  electric 
resistance  is  of  the  nature  of  velocity,  its  real  nature 
being  unknown. 

A  by-path  or  shunt  is  often  employed  with  a  galvan- 
ometer or  other  device  which  may  carry  too  much 
current. 

By  the  multiplying  power  of  a  shunt  is  meant  the 
ratio  in  which  the  shunt  reduces  the  current  through  the 
device  shunted  and  is  represented  by  unity  plus  the  ratio 
of  the  resistance  of  the  device  to  the  resistance  of  the 
shunt. 

A  very  small  leakage  in  a  high  resistance  apparatus 
may  materially  reduce  the  resistance  proper  to  that  appa- 
ratus. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 
WEEKLY. 


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AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED     GRADE. 

KLKCTRIC  CURRKNT. 


40.  It  is  a  popular  belief  that  an  electric  current  con- 
sists actually  of  the  passage  of  electricity  through 
a  conductor.  Like  most  popular  beliefs  this  is  erroneous. 
According  to  modern  views,  when  a  telegraph  circuit, 
say,  between  New  York  to  Philadelphia,  has  an  E.  M.  F. 
impressed  upon  its  terminals  at  New  York,  it  is  no  longer 
believed  that  electricity  leaves  the  electromotive  source 
or  dynamo  and  flows  through  the  conductor  to  Phila- 
delphia like  water  through  a  pipe.  When  an 'electromo- 
tive source,  such  as  a  battery,  is  placed  on  open  circuit, 
it  produces  in  the  surrounding  ether  a  certain  small 
electric  stress.  When,  however,  the  conducting  line  or 
circuit,  which  may  be  100  miles  long,  is  connected  to 
its  terminals,  this  electric  stress  breaks  down  in  the  ether 
around  the  battery,  and  a  flow  of  energy  in  the  form 
of  an  electro-magnetic  wave  moves  outward  from  the 
battery  around  and  along  the  surface  of  the  wire,  with 
the  velocity  of  light.  According  to  this  view,  the  real 

Published  by 

THE   ELECTRICAL  ENGINEER, 
203  Broadway,  New  York,  N.  Y. 

[Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  June  14,  1894.] 


42 


province  of  the  conductor  is  to  direct  the  flow  of  energy 
from  the  battery,  the  conductor  acting  as  a  sink  or  line  of 
absorption  in  the  dielectric  medium,  and  determines  the  di- 
rection of  movement  of  the  energy.  A  conductor,  there- 
fore, directs  the  passage  of  energy  through  the  medium, 
at  the  same  time  expending  some  of  that  energy  in  pro- 
gress, converting  it  into  heat  within  the  substance  of  the 
wire.  The  electric  current  cannot,  consequently,  be  con- 
veniently regarded  as  passing  through  the  wire,  but 
rather  through  the  ether  surrounding  the  wire,  the 
energy,  as  it  moves  forward,  converging  and  being  rained 
down  upon  the  wire. 

However  true  this  theory  may  be,  and  it  is  in 
general  acceptance  by  the  advanced  thinkers  of  to-day, 
it  is  much  more  convenient  for  practical  purposes  to 
retain  the  old  notions  concerning  the  passage  of  a  cur- 
rent through  the  wire  like  water  through  a  pipe,  since 
the  effects  of  electric  currents  can  be  more  readily  dealt 
with  by  the  simpler  theory  than  by  one  which  is  probably 
more  nearly  correct. 

41.  When  an  electromotive  force  is  impressed  on 
a  condenser,  energy  enters  the  dielectric  and  the 
condenser  receives  an  electric  charge,  a  certain  quantity 
of  electricity  entering  the  condenser.  The  unit  of  elec- 
tric quantity  is  called  the  coulomb.  While  the  electric 
charge  is  entering  the  condenser,  its  time-rate-of-change 
is  called  the  electric  flow  or  current.  A  time-rate-of- 
change  of  one  coulomb  per  second  is  called  an  ampere. 
If  q,  be  the  quantity  of  electricity  or  charge,  in  coulombs, 
which  is  entering  the  conductor  or  passed  through  a  con- 
ducting circuit,  and  /,  be  the  strength  of  current  in 


43 


amperes,  flowing  through  the  conductor,  then  at  any 
instant, 

^~3T 

that  is,  a  current  is  the  time-rate-of-change  of  the  quan- 
tity, or  the  instantaneous  rate  of  flow.1 

When  a  quantity  of  electricity  moves  through  a  cir- 
cuit under  the  action  of  an  electromotive  force,  work  is 

1.  For  the  sake  of  readers  who  have  not  yet  mastered  the  elements 
of  differential  calculus,  the  following  explanation  of  the  symbols  here 
employed  may  be  acceptable.  If  Jti  be  the  space  passed  through  by  a 
moving  body,  reckoned  from  a  given  instant  of  time,  then  if  the 
spaces  moved  over  in  equal  intervals  of  time  be  equal,  the  body  will 
be  moving  with  uniform  velocity,  and  the  length  of  any  portion  of  its 
path,  divided  by  the  time  required  to  describe  it,  will  always  give  the 
same  value  of  the  velocity.  Thus,  if  the  body  be  moving  with  the 
velocity  of  20  feet  a  second,  the  quotient  of  any  distance  it  has 
moved  over,  divided  by  the  time  occupied  in  travelling  though  it,  will 
always  be  equal  to  20;  but  if  the  velocity  of  the  body  be  varying,  the  quo- 
tient of  the  space  traversed  by  the  time  occupied  in  traversing  will  gen- 
erally be  different.  Thus,  a  body  falling  to  the  ground  from  rest,  is 
continually  accelerating  its  velocity,  and  the  quotient  of  space  by  time 
will  vary,  not  only  with  the  position  of  space  selected,  but  also  with 
the  length  of  the  space  traversed.  The  velocity  at  any  point  of  its 
descent  is,  therefore,  only  to  be  defined  by  the  quotient  of  space  tra- 
versed by  time  occupied  in  traversing,  for  an  extremely  short,  and  in 
theory,  for  an  infinitely  short,  distance.  For  this  conception  a  special 

symbol  is  introduced;  thus,  if  —  =  ®,  be  the  velocity  of  a  body,  and 

different  values  of  S,  divided  by  their  appropriate  intervals  of  t,  give 
different  values  of  ® ;  then,  proceeding  to  the  ideal  infinitely  small  spaces 
and  the  infinitely  short  intervals  of  time  in  traversing  it,  which  may  be 
represented,  respectively,  by  the  symbols  d  #,  and  d  t,  the  true  velocity 

at  any  moment  is  expressed  as  before,  by  the  quotient  ®  =  —  . 

d  t 

A  similar  method  is  adopted  for  dealing  with  all  variable  quantities 
whose  rates  of  variation  are  not  constant.  As  for  example,  in  the 

case  before  used  in  the  context,  where  amperes  =  — ? .     Here  the 

d  t 

quantity  of  electricity  varying  perhaps  irregularly  with  time,  shows 
that  the  current  may'  not  have  the  same  value  at  different  times,  but 

the  symbol  — ^L  gives  us  a  means  of  expressing  the  actual  instantane- 

it    t 

ous  value  at  any  moment. 


44 


done,  just  as  when  a  mechanical  force  moves  through  a 
distance.  If  the  quantity  of  electricity  moved  is  known 
in  coulombs,  and  the  force  with  which  it  is  moved  in 
volts,  their  product  will  represent  the  volt-coulombs  or 
the  joules  of  work  expended  in  the  process,  so  that 

W  =  E  q  joules. 

If  now  we  know  the  rate  per  second  at  which  the  quan- 
tity is  flowing  or  ^7  >  the  current  strength  in  amperes, 

and  multiply  this  by  the  E.  M.  F.,  we  obtain  the  volt- 
amperes  or  the  activity  of  the  circuit  in  watts, 

d  W 

-jj  —  P  =  El  watts. 

In  mechanics  the  activity  of  a  force  is  measured  by 
the  product  of  the  force  and  the  distance  through  which 
it  acts  or 

P  =  F  -=—  cos  a  ergs  per  second  ;* 
d  t 

where  /*,  is   the   activity ;  F,  the  force   in   dynes; -^ 

the  time  rate  of  displacement  in  cms.  per  second  ;  and  a 
the  angle  between  the  directions  of  displacement  and 
the  direction  of  the  force.  So  in  electricity, 

P  =  E  ~2  cos  a  (watts) ; 
d  t 

d  o 
where  P,  is  the  activity,  K  the  E.  M.  F.  in  volts,  ^   the 

current  strength,  and  a  the  angle  between  the  direction 

1.  The  symbol  cos  a,  represents  the  cosine  of  the  angle  a,  and  is  always 
some  number  between  minus  one  and  plus  one,  which  can  be  found 
for  any  given  angle  from  trigonometrical  tables.     For  example,  if  <i 
60°,  cos  60°  =  0.5;  so  that  in  this  case  the  number  O.fi  might  be  sub- 
stituted for  the  symbol  cos  a 


45 

of  the  E.  M.  F.  and  the  current.     In  almost  all  cases  the 
current  and  E.  M.  F.  are  in  the  same  line,  so  that  cos  a 

becomes  unity,  and  P  =  E  (Li  =  E 1. 


42.  Although  the  coulomb,  or  ampere-second,  is  the 
unit  of  electric  quantity,  yet  the  ordinary  com- 
mercial unit  of    electric  quantity  is  the   ampere-hour. 
This  is  because  the  second  is  a  too  small  a  unit  of  time  for 
practical  use.    The  ampere-hour,  is  3,600  coulombs ;  i.e., 
the  number  of  seconds  in  an  hour. 

43.  When  a  uniform  conductor  in  the  form  of  a 
wire  has  a  cross-section  of,  say,  0.6  sq.  cm.  and 

carries  a  steady  current  of  15  amperes,  the  current  den- 

,i  /> 
sity  would  be  -^  =  0.04  ampere  per  square  centimetre, 

J.O 

and  would  be  uniform  for  the  entire  cross-section  of  the 
conductor.  Current  density  is,  therefore,  the  intensity 
of  current  per  normal  unit  area,  and  is  expressed  in  am- 
peres per  square  centimetre. 

44.  Attempts  have  at  different  times  been  made  to 
formulate  rules  for  the  carrying  capacity  of  con- 
ductors and  of  copper  wires  by  specifying  a  definite  cur- 
rent density,  for  example,  1,000  amperes  per  square  inch 
of  cross-section.     Such  a  rule,  however,  cannot  prescribe 
uniform  temperature  elevations  in  conductors  of  differ- 
ent sizes,  for  the  reason  that  the   surface  of  the  con- 
ductor only  increases  as  the  square  root  of  the  cross- 
sectional   area,    and    the   surface  area   is   the  principal 
factor  determining  the  rate  of  escape  of  heat  from  the 
wire. 


46 


45.  When  the  strength  of  a  current  is  rapidly  alter- 
ing, as  in  pulsatory  or  alternating  currents,  it  be- 
comes necessary  to  define  how  that  varying  current 
strength  shall  be  estimated. 

For  example,  the  mean  magnetic  strengtli  of  that  cur- 
rent or  the  mean  electrolytic  effect  of  that  current  might 
be  taken  as  determining  its  value.  In  these  cases,  the 
strengtli  would  be  the  arithmetical  mean  or  average  of 
the  current  strength  in  amperes  during  the  time  under 
consideration.  In  practice,  however,  rapidly  varying 


FIG.  13. — THOMSON  MIRROR  GAL-     FIG.  14. — THOMSON  MARINE  GAL- 

VANOSCOPE     FOR     SIGNALLING  VANOMETER  FOR  USE  ON  R.OLL- 

ON  SUBMARINE  CABLES.  ING  VESSEL  AT  SEA. 

currents  are  measured  by  their  mean  heating  effects,  and 
since  the  heating  effect  of  a  current  depends  upon  the 
square  of  its  strength,  currents  are  determined  in  their 
effective  values  by  the  average  of  their  squares  taken 
during  the  period  under  consideration.  If  half  an  am- 
pere of  continuous  current  just  suffices  to  heat  the  fila- 
ment of  an  incandescent  lamp  up  to  a  certain  degree  of 
incandescence,  then  any  rapidly  pulsatory  or  alternating 
current  which  will  bring  the  lamp  to  the  same  degree  of 
incandescence  is  just  half  an  ampere  in  strength. 


47 


46.  Various  methods  may  be  employed  for  measur- 
ing the  strength  of  an  electric  current,  but  prac- 
tically the  magnetic  method  alone  is  employed. 

When  an  electric  current  passes  through  a  conductor, 
it  is  accompanied  by  the  distribution  of  magnetic  flux  or 
magnetism  in  its  vicinity.  This  flux  is  attended  by 
stresses  in  the  space  so  occupied,  which  stresses  acting 
either  on  iron  or  active  conductors,  produce  movements 


Fiu.  15. — HIGH-GRADE  THOMSON  MIRROR  GALVANOMETER  FOR 
MEASURING  HIGH  INSULATION  RESISTANCES. 

in  the  same,  which  movements  are  opposed  by  springs 
or  gravitational  forces.  The  amount  of  motion  pro- 
duced is  usually  read  off  by  a  pointer  or  index  upon  a 
graduated  scale. 

Fig.  13  shows  a  common  form  of  Thomson  mirror 
galvanoscope  employed  for  the  reception  of  telegraph 
signals  on  long  submarine  cables.  A  circular  coil  of 
wire  in  the  upper  part  of  the  instrument  carries  at  its 


48 


centre  a  small  magnetic  needle  attached  to  the  back  of  a 
small  glass  mirror,  and  suspended  on  a  fibre. 

Fig.  14  shows  a  form  of  this  instrument  intended  for 
use  on  board  ship.  The  coil  and  mirror  are  enclosed  in 
a  soft  iron  case  one  inch  thick,  in  order  to  reduce  as  far 
as  possible  the  disturbing  effect  of  the  earth's  magnetic 
field  on  the  suspended  magnet  when  the  ship  turns  about. 

Fig.  15  shows  a  form  of  double  coil  Thomson  galvan- 
ometer prepared  for  careful  insulation  tests.  The  coils 
are  supported  on  long  corrugated  hard  rubber  pillars. 

SYLLABUS. 

It  is  no  longer  believed  that  electricity  flows  through 
a  conductor  but  rather  through  the  dielectric  surround- 
ing the  conductor. 

The  presence  of  a  conductor  directs  the  energy,  and  at 
the  same  time  absorbs  some  of  it  in  progress. 

The  unit  of  electric  quantity  is  called  the  coulomb. 

The  time  rate  of  change  in  quantity  that  has  passed 
through  a  circuit  is  the  current  in  that  circuit,  and  is  ex- 
pressed in  units  called  amperes. 

The  unit  of  electric  quantity,  the  ampere-second  or 
coulomb  is  not  used  in  commercial  practice,  being  re- 
placed by  the  ampere-hour. 

The  density  of  electric  current  is  expressed  in  am- 
peres per  square  centimetre.  It  is  uniform  only  in  the 
case  of  steady  currents,  and  that  only,  where  the  conduc- 
tors are  very  long  and  are  uniform  in  nature  and  cross- 
section. 

Galvanoscopes  are  used  to  indicate  the  presence  of  a 
current,  and  galvanometers  to  measure  its  strength. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia, 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 


WEEKLY. 


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AND 

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ADVANCED 

OHM'S 


47.       Ohm's  law   as  discovered  and  annunciated  by 

Dr.  Ohm  of  Berlin  in  1825,  is  generally  expressed 

as  follows :     The    current  strength    in   any  continuous 

current  circuit  is  directly  proportional  to  the  total  E.  M.  p., 

and  inversely   proportional  to    the   total   resistance,  or 

('  =  ~;  or,  as  written  in  foreign  countries,  /  =  _     (1.) 
R  H 

Ohm's  law,  as  expressed  above,  assumes  that  the  full 
current  strength  in  the  circuit  has  been  reached.  Strictly 
speaking,  a  continuous  current  requires  an  indefinitely 
long  time  to  attain  full  strength,  although  practically, 
within  the  limits  of  measurement,  the  maximum  strength 
is  usually  reached  in  a  small  fraction  of  a  second. 

At  the  International  Electrical  Congress  at  Chicago 
in  1893,  it  was  recommended  that  a  uniform  system  of 
notation  should  be  internationally  adopted,  and  since  the 
symbol  /was  selected  for  current  strength  in  this  nota- 

Published  by 

THE   ELECTRICAL   ENGINEER, 
203  Broadway,  New  York,  N.  Vr    *  «. 

[Entered  as  second-class  matter  at  the  New  York,  N,  Y.,  Post  Office,  June  14, 


1894.] 


50 


tion,  and  (7,  for  capacity,  we  propose  to  follow  the  inter- 
national notation.  From  equation  (1)  we  obtain, 

E  =  IR  (2.) 

and  R^^  (3.) 

so  that  in  any  continuous  current  circuit,  any  two  of  the 
essential  quantities,  (electromotive  force,  resistance  and 
current)  being  known,  the  third  can  be  determined. 

48.  These  formulae  apply  not  only  to  a  complete 
circuit,  but  also  to  any  portion  of  the  same.  Thus  the 
electromotive  force  in  a  circuit  distributes  itself  in  such 
a  manner  that  the  current  strength  in  the  circuit  is  equal 
throughout.  The  electromotive  force  required  to  drive 
a  current  through  any  portion  of  a  circuit  against  the 
resistance  in  that  portion,  is  usually  called  the  "drop" 
in  that  circuit.  Thus  with  a  dynamo  supplying  a  con- 
tinuous current  at  a  pressure,  across  the  brushes,  of  125 
volts,  to  incandescent  lamps  in  parallel,  it  may  be  required 
to  limit  the  drop  in  the  supply  mains  to  eight  per  cent,, 
meaning  that  eight  per  cent,  of  the  125  volts,  or  ten 
volts,,  would  be  the  limit  of  pressure  required  to  drive 
the  supply  current  through  the  mains,  leaving  115.0 
volts  at  the  lamps. 

If  the  total  number  of  lamps  was  500,  each  of  50 
watts,  and  since  the  product  of  the  current  consumed 
and  E.  M.  F.  delivered  is  the  activity  in  the  lamp,  the  cur- 
rent supplied  to  each  lamp  would  be  -ff^  =  0.4348 
amperes,  so  that  the  total  current  is  500  X  0.4348  =  217.4 
amperes,  representing  a  total  activity  of  115  X  217.4 
=  25,000  watts,  or  25  K.  w.  The  drop  of  ten  volts 
allowed  in  the  two  conducting  wires,  or  five  volts  in 


51 


each    wire,  requires   that   the   resistance   of   each   wire 

should   in   conformity   with  the   formula,  r   —  —  ,  be 

?, 

=  0.023  ohm.     The  resistance  of  each  lamp  must 
217.4 

in  conformity  with  the  same  law  be, 

r  =  —  =     115     =  264.4  ohms. 
i         0.4348 

The  joint  resistance  of  all  the  lamps  is,  =  -^—  =  0.5288 

ouU 

ohm. 

If  the  resistance  of  the  dynamo  be  0.015  ohm,  the 
drop  in  the  dynamo  must  also  be  0.01  5  X  217.4  =  3.26 
volte,  so  that  the  E.  M.  F.  in  the  circuit  must  be  125  -f- 
3.26  =  128.26. 

The  total  resistance  in  the  circuit  would  be, 

Dynamo  armature  ...............  0.015  ohm. 

.     Leads  ..............  2  X  0.023  =  0.046     " 

Lamps  ........................  0.5288  " 

0.5898  " 
So  that  the  total  current  in  the  circuit  would  be 

128.26 


The  activity  in  the  circuit,  7^=217.4X128.26=27.884  K.  w. 

Of  this  the  activity  in  the  dynamo  is,  IeY  =21  7.4x3.  26=  0.709  K.  w. 
The  activity  in  the  leads  is,  .Zfc2+03)=217.4XlO=  2.175    ." 
The  activity  in  the  lamps  is,        /04=217.4x  115=25.000     " 

27.884     " 

The  electrical  efficiency  of  distribution  is  the  ratio  of 
the  energy  in  the  lamps  to  the  energy  in  the  circuit  or 


52 


49.  Applying  the  same  law  to  branch,  derived  or 
shunt  circuits,  the  current  in  any  particular  branch 
is  equal  to  the  electromotive  force  at  the  terminals  of  that 
branch,  divided  by  its  resistance.  Thus  in  the  preceding 
figure,  the  current  in  any  one  lamp,  is  115  volts  divided 
by  264.4  ohms  =  0.4348  ampere.  This  is  true  no 
matter  how  complex  the  network  of  conductors  may  be. 


FIG.  16. — APPLICATION  OF  OHM'S  LAW  TO  A  CIRCUIT. 


50. 


In  complete  networks  of  circuits,  there  are  cer- 
tain corollaries  of  Ohm's  law  which  enable  the 
current  strength  to  be  deduced  in  any  branch.     These 
may  be  expressed  as  follows  : 

(1.)  No  current  can  be  absorbed  at  any  branch  point. 
Thus  in  Fig.  17,  il=is-\-iB  because  if  this  identity  did  not 
hold,  the  current  arriving  at  the  point  A,  would  be 
greater  or  less  than  the  current  leaving  it,  so  that  gen- 
eration or  absorption  of  current  would  occur  at  the 
point  A. 


(2.)  The  total  E.  M.  F.  in  any  closed  loop  must  be  equal 
to  the  sum  of  the  potential  differences  in  the  loop  due 
to  IE. 

Thus  in  Fig.  1 7,  E —  e  —  %  r^  +  is  rs  —  it  r4  -|-  4  /'5, 
because  if  this  identity  did  not  hold,  the  total  E.  M.  F. 
acting  in  the  loop  would  be  greater  or  less  than  the  total 
counter  E.  M.  F.  of  1R  established  by  the  current, 
whereas,  in  any  continuous  current  loop  or  circuit,  these 
two  quantities  must  be  equal. 

(3.)  The  P.  D.  at  the  extremities  of  any  line  must  he 
equal  to  the  sum  of  the  P.  D'S  due  to  IR,  in  that  line  to- 
gether with  the  sum,  of  E.  M.  F.'S  contained  in  it. 


E 

FIG.  17.  —  NETWORK  OF  CONDUCTORS. 

Thus   calling  17,  the   potential  difference  between  A 

and  B 

e. 


This  follows  by  the  same  reasoning  as  in  the  preceding 
case,  of  which  it  is  a  direct  consequence,  for,  U  =E-  —  i±  r^ 

(4.)  The  current  in  any  ~branch  is  the  sum  of  the  cur- 
rents that  all  the  E.  M.  F.'S  in  the  network  would  produce 
if  each  of  the  E.  M.  F.'S  were  successively  permitted  to  act 
dngly. 

Thus  calling  im  the  current  which  would  be  establish- 
ed in  rs  if  the  E.  M.  F.,  6,  existed  alone,  and  an,  the  cur- 
rent which  would  be  established  in  /'3,  if  ^existed  alone, 


then,  when  both  E.  M.  F.'S  exist,  as  shown  in  the  figure, 
the  resulting  current  is  =  im  -\-  in. 

(5.)  Taking  any  two  branches  such  as  r8  and  r5,  the 
current  which  would  be  set  up  in  r5  by  inserting  a  given 
E.  M.  F.  in  7*3,  is  equal  to  the  current  strength  which 
would  be  set  up  in  rs  by  the  insertion  of  the  same  E.  M.  F. 
in  r5. 

Thus  considering  the  figure  as  representing  the  co'n- 
nections  of  a  Wheatstone  bridge,  the  current  set  up  in 
the  galvanometer  branch  r4  by  the  testing  battery  in  £„ 

0.47  VOLTS 
r«=  3.135  OHM 


!^                             3.O23  AMP^ 
f    ±                          %  =3.135  OHM 

r«  -H 

h-114.4  V<5LTS-^ 

37.857  OHMS 

2 

HUH 

44.167  OHMS 

X^                                      <  O.356  AMP. 

-^                                8.36  VOLTS 
^                                r5  =  3.135  OHM 

P7 
t—  1  1  7.  8  VOLTS-> 

I 

STJTJ 

. 

<2.667  AMP. 

FIG.  18.— THREE-WIRE  SYSTEM. 

is  equal  to  the  current  which  would  be  set  up  in  TI 
by  removing  the  testing  E.  M.  F.  to  r4. 

These  rules  can  all  be  deduced  directly  from  Ohm's 
law.  Numbers  (1)  and  (2)  are  frequently  called  Kirchoff 's 
laws.  In  all  cases  care  must  be  taken  to  observe  the  di- 
rections of  the  various  E.  M.  F.'S  and  currents,  since  the 
geometrical  and  not  the  mere  arithmetrical  sums  of  these 
quantities  are  under  discussion.  Also  the  E.  M.  F.'S  must 
be  considered  independently  of  the  resistance  which 
practically  accompany  them.  In  (5)  for  example,  when 
we  consider  the  transference  of  the  E.  M.  F.  in  a  battery, 


55 


we  have  to  regard  the  resistance  of  the  battery  as  im- 
movable, and  the  E.  M.  F.  only  to  be  transferred. 

51.  In  order  to  determine  the  current  strength  in 
any  or  all  the  n  branches  of  a  conducting  net- 
work in  which  all  the  E.  M.  F.'S  and  resistances  are  known, 
it  is  customary  to  write  down  n  independent  simultaneous 
equations  with  the  aid  of  (1)  and  (2),  and  then  solve 
these  equations  by  the  ordinary  algebraic  processes. 
Thus  Fig.  18  represents  the  connections  of  a  "three- 
wire  system"  in  which  two  dynamos  in  series  operate 
two  groups  of  incandescent  lamps  with  a  "  neutral " 
wire  from  the  connection  of  the  dynamos  to  the  con- 
nection of  the  lamp  groups.  We  may  determine  the 
current  strength  in  the  various  conductors  as  follows : 

'*/!  =  ^  (/'3  +  /*6)  +  14  r4 

%  =  4  (r&  +  r?)  —  i4  r4 

%  =  i*  +  k 
Solving  these  equations  for  i%,  i4  and  i-M  we  obtain 

_  ff>4  +   %   £* 

"  r<  (E,  +  B,)  +  ^i  £* 

'    _  't-h  R*  —  U>2  RI  /rx 

"  n  (B,  +  Bj  +  Bl  E, 

U  r4  -{-  u2  R^  ,  x 

"  r4  (R,  +  B,)  +  B,  //,, 

wliere  P^  —  (/'3  +  r6);  R,  =  (/v,  +  /•,);  and  tf=ul-\-  y/2 
It  follows,  therefore,  from  (J),  that  whatever  the  two 
resistances  r«  and  /v,  may  be,  that  is  to  say,  whatever  the 
two  incandescent  lamp  loads  may  be,  balance  in  the  sys- 
tem will  be  obtained,  and  no  current  will  flow  through  v4 
when  M!  :  <i,»  ::  B1  :  R%. 

For  example,  suppose  (Fig.  18)  that  the  positive  load 


56 


consists  of  seven  lamps  of  265  ohms  each,  and  the  nega- 
tive load  of  six  lamps  of  265  ohms  each,  while  the  pres- 
sure at  dynamo  terminals  is  125  volts  =  U{  =  u^  and  the 
resistance  of  each  conductor  =  3.135  ohm. 

Then  r%  =  37.857  ohms,  and  r?  =  44.167. 
E,  =  40.992     "        "  Rz  =  47.302. 
Then  by  («\  t,  =  -  -^X  3.135  +  125  X  47.302 

3.135   X   88.294  +  40.992   X  47.302 


*6    = 

ii  = 

2.667 
0.356 

The  drop  in 
Pressure  at 

rs  = 

A   =: 
B   := 

9.47    volts. 
8.360     " 
114.38       " 
117.79       " 

250.00 

SYLLABUS. 

The  current  strength  in  any  continuous  current  cir- 
cuit after  full  strength  has  been  attained,  is  directly  pro- 
portional to  the  total  E.  M.  F.,  and  inversely  proportional 
to  the  total  resistance.  This  is  called  Ohm's  Law. 

Ohm's  law  applies  not  only  to  an  entire  circuit,  but 
also  to  any  part  of  a  circuit. 

The  fall  of  pressure  or  "drop'1  in  a  conductor  carry- 
ing a  current  is  the  pressure  required,  to  drive  the  current 
through  the  conductor,  and  is  equal  to  I R,  the  product 
of  the  current  and  the  resistance. 

Laboratory  of  Houston  &  Kennelly. 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 
WEEKLY. 

No.  8.  AUGUST  4,  1894. 

Electrical   Engineering   Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED     GRADE. 

ELBCTRIC    CIRCUITS 


52.  The  term  circuit,  as  generally  understood,  em- 
braces  a   complete   conducting   path  established 

between  the  electric  source  and  the  electro-receptive  de- 
vices that  in  practice  are  connected  therewith.  Ordinarily, 
the  circuit  consists  of  a  true  conducting  path,  principally 
or  wholly  of  metal ;  but  circuit  paths  may,  however,  lie 
through  a  non-conducting  dielectric,  as  in  the  case  of  the 
dielectric  circuit.  In  the  electric  circuit,  the  current 
strength  may  be  unvarying ;  in  the  dielectric  circuit,  it 
can  never  be  uniform.  All  conducting  circuits  belong 
to  the  former  type ;  all  electrostatic  circuits,  to  the  latter 
type. 

53.  Conducting  circuits  may  be  conveniently  grouped 
into  four  general  classes ;  namely, 

(1.)  Series  circuits. 
(2.)  Multiple  circuits. 
(3.)  Multiple-series  circuits. 
(4.)  Series-multiple  circuits. 

Published  by 

THE  ELECTRICAL  ENGINEER, 
203  Broadway,  New  York,  N.  Y. 

[Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  June  14,  1894.! 


58 


54.       In   the   series   connection    of    electro-receptive 

devices,  the  separate  devices  are  placed  so  as  to 

be  successively  traversed  by  the  current.     The  current 

strength  is  maintained   constant   no   matter  how  many 


FIG.  19. — SERIES  CIRCUIT. 

separate  devices  are  included  in  the  circuit ;  consequently, 
in  all  such  cases,  the  electromotive  force  of  the  source 
must  be  varied  in  accordance  with  the  number  of  devices 
in  circuit.  This  variation  is  generally  obtained  auto- 
matically from  constant-current  dynamos. 

Fig.  19  shows  a  dynamo  of  E.  M.  F.,  E,  connected  with 
a  number  of  electro-receptive  devices  connected  by  the 
conducting  circuit  rl9  etc.  Here  the  total  resistance  of 
the  circuit  is  (^  +  ^4.  .  .  .  +JSs)+(r1  +  r2+ .  .  .  +  r8) 
and  the  current  in  the  circuit  is  equal  to  the  E.  M.  F.,  E, 
divided  by  this  resistance.  Calling  this  current  7,  the 
activity  yielded  by  the  source  is  ^/watts,  and  the  activity 
in  any  separate  device  is  P  It,  developed  entirely  as 
heat,  while  the  activity  in  any  section  of  conducting  wire 
is  P  r ;  so  that  the  activity  in  the  circuit  is  entirely  ex- 


FIG.  20. — SERIES  CIRCUIT  CONTAINING  COUNTER  E.  M.  F. 

pended  in  producing  heat  either  in  the  receptive  devices, 
or  in  the  conducting  wires  connecting  the  same.  Such 
activity  is  commonly  called  P  7?,  activity,  and  the  loss 
of  energy  accompanying  such  currents  is  the  P  R,  loss. 


59 


Fig.  20  shows  a  dynamo  of  E.  M.  F.,  E,  connected  in 
series  with  a  number  of  electro-receptive  devices  each  of 
which  supplies  not  only  the  resistance  7?,  but  also  a  counter 
electromotive  force  e.  The  resistance  in  this  circuit  is 
obtained  as  in  the  preceding  case,  but  the  current  is  now, 


the  activity  yielded  by  the  dynamo  to  the  external  cir- 
cuit is  E  /,  watts  as  before,  but  the  energy  liberated  in 
each  device  is  now  (/2  R  -j-  e  /)  watts.  The  first  term 
is  entirely  thermal,  but  the  energy  corresponding  to  the 
second  term  may  be  mechanical,  chemical,  or  thermal, 


FIG.  21.  —  MULTIPLE  CIRCUIT. 

depending  upon  the  nature  of  the  receptive  device.  In 
the  case  of  the  arc  lamp,  e  I,  is  thermal  ;  in  the  case 
of  the  magnetic  device,  e  /,  is  generally  mechanical  ;  and 
in  the  case  of  electrolysis,  e  /,  may  be  partly  mechanical, 
but  is  principally  chemical. 

55.  In  the  multiple  connection  of  electro-receptive 
devices,  all  the  positive  terminals  of  the  devices 
are  connected  to  a  single  positive  lead,  and  all  the  nega- 
tive terminals  similarly  connected  to  a  single  negative 
lead.  Thus  in  Fig.  21  a  number  of  receptive  devices 
represented  by  the  resistances  EI?  Ba,  etc.  are  connected 
as  shown  with  the  positive  and  negative  leads  respec- 
tively of  the  dynamo  of  electromotive  force  E.  In  this 


UITI7BESIT7 


60 


case  the  resistance  of  the  circuit  is  the  complex  expres- 
sion obtained  in  the  following  manner  :  — 

The  resistance  at  E,  7?K  =  R$. 

The  resistance  at  D,  R^  =  _  _ 


Resistance  at  C  =  R   = 


56.       In  the  multiple-series  connection  of  electro-re- 

ceptive devices,  the  electro-receptive  devices  are 

connected  in  series  groups,  and  these  groups  subsequently 


< Elec.Engineer 

FIG.  22. — MULTIPLE  SERIES  CIRCUIT. 

connected  in  parallel.  Thus  in  Fig.  22,  a  number  of  re- 
ceptive devices  rl9  r^  etc.,  are  connected,  as  shown,  in 
three  separate  groups  in  series,  and  these  groups  sub- 
sequently connected  in  multiple.  If  Hl9  R^  R^  and 
RI,  are  the  resistances  of  each  group,  then  the  total  joint 
resistance  of  the  circuit 

_  1 ,         _,         _. 


57.       In  the  series-multiple  connection  of  receptive  de- 
vices, the  separate  devices  are  connected  in  groups 
in  multiple,  and  these  separate  groups  subsequently  con- 
nected in  series. 


61 


Such  an  arrangement  is  indicated  in  Fig.  23,  where 
four  groups  of  four  lamps  each  are  operated  in  series.  By 
this  means  the  current  in  the  supply  mains,  for  a  given 
number  of  lamps  equally  divided  into  groups,  is  reduced 
four  times,  and  the  operating  pressure  at  main  terminals 
is  increased  four  times.  Such  an  arrangement,  with  the 
addition  of  the  equalizing  wires  c  D,  E  F,  and  G  H,  is 
practically  employed,  and  is  called  &  five-wire  system. 

58.  All  E.  M.  F.'S  developed  in  a  circuit  by  a  con- 
tinuous current  are  counter  E.  M.  F.'S.  A  current  /, 
flowing  through  a  resistance  It,  sets  up  a  virtual  counter 
E.  M.  F.  of  /  It,  volts.  When  flowing  through  an  elec- 


A 

B 

4 

$  O  4 

+3f 

0000 

VG 

0000 

•t'i' 

oooo 

j 

Elec.  Engineer   K 

FIG.  23. — SERIES-MULTIPLE  CIRCUIT. 

trolyte  it  usually  establishes  a  counter  E.  M.  F.  of  polari- 
zation. When  passing  through  a  coil,  loop,  or 
electromagnet,  it  sets  up,  during  the  initial  period  of 
rise  to  full  strength,  a  counter  E.  M.  F.  of  induction,  as 
will  be  subsequently  explained.  When  it  passes  through 
a  motor  and  causes  its  armature  to  rotate,  it  develops  in 
the  rotating  armature  a  counter  E.  M.  F.  In  all  these 
cases  the  current  does  work  upon  the  counter  E.  M.  F. 
and  expends  that  work  as  heat  in  the  resistance,  as 
chemical  energy  in  the  electrolyte,  as  magnetic  energy 
sometimes  taking  the  form  of  mechanical  work  in  the 
coil  or  magnet,  and  as  mechanical  work  in  the  rotating 
motor. 


If  the  E.  M.  F.  developed  in  a  circuit  by  a  current  were 
not  a  counter  E.  M.  F.  but  aided  the  current,  it  would 
do  work  on  the  current.  This  work  would  have  to  be 
drawn  from  the  source  of  the  aiding  E.  M.  F.,  so  that  it 
would  be  only  necessary  to  expend  some  work  in  the 
circuit,  to  involve  the  expenditure  of  additional  work 
from  some  other  portion  or  portions,  indicating  a  condi- 
tion of  unstable  electrical  equilibrium. 

In  all  cases,  therefore,  where  work  is  done  in  a  circuit 
by  the  action  of  a  current,  that  work  is  due  to  the  de- 
velopment and  action  of  a  counter  E.  M.  F.  and  the 
greater  this  counter  E.  M.  F.  for  a  given  current  strength, 
the  greater  the  amount  of  energy  that  is  absorbed  by  its 
source,  and  the  greater  the  amount  of  work  which  may 
be  expended.  A  counter  E.  M.  F.  is,  therefore,  not  pre- 
judicial to  the  action  of  an  electric  source.  On  the  con- 
trary, it  is  the  means  by  which  work  can  be  delivered  to 
the  circuit. 

59.       The  preceding  facts  may  be  tabularly  arranged 
as  follows : 

VARIETIES  OF  COUNTER  E.  M.  F.  DEVELOPED  BY 
ALTERNATING  OR  CONTINUOUS  CURRENTS. 


Varieties  of  E.  M.  F. 

Types. 

Varieties  of  Energy. 

1.  Virtual  Counter  E.  M.  F  
2    Counter  E  M  F  of  Polarization 

(IS)..,, 
(e) 

(IR}I=1*  R=  Heat 
in  Resistance. 
(e  1  )  —  chemical  energy 

3.  Counter  E.  M.  F.  of  Induction..  . 
4.  Motor  E.  M.,  F  

(e)  
(e)  

in  electrolyte. 
(e  1)  =  magnetic  energy 
and  mechanical  work 
in  coil  in  magnet. 
(e  /)  —  mechanical  work 

in  rotation  of  motor. 

63 


60.       Ohm's  law  is  essentially  the  law  applying  to  any 
circuit  or  to  any  conductor  forming  portion  of  a 

circuit.     The   fundamental  law  which  underlies  the  ex- 

-p< 
pression  I  =  -= -  is,  however,  as  follows, 

Ji 

£=±9oT0gi 

where  i  is  the  current  density  at  any  point  of  a  circuit, 
ea  the  E.  M.  F.  at  that  point,  being  considered  as  a  vector 
or  directed  quantity,  and  being  also  equal  to  the  drop  of 
pressure  per  centimetre  of  length,  ^,  the  resistivity  of  the 
medium  at  that  point,  and  </,  its  reciprocal,  the  conduct- 
ivity. This  law,  therefore,  expresses  the  fact  that 
Avherever  the  electromotive  force  is  acting,  the  current 
density  is  in  direction  of  that  E.  M.  F.,  and  equal  to  the 
value  of  that  E.  M.  F.  multiplied  by  the  local  value  of  ^, 
the  conductivity.  This  is  Ohm's  law  expressed  for 
localized  action  and  not  for  generalized  action. 

The  formula  J- =^ 

is  generally  employed  with  the  practical  units  of  the  am- 
pere, ohm  and  volt.  It  is  evident,  however,  that  it  is  also 
applicable  to  the  fundamental  c.  G.  s.  units.  So  that  when 
J?is  expressed  in  units  of  10  bicro volts,  or  10~8  volts,  and 
7?  in  bicrohms  ;  i.  e.,  10~9  ohms,  the  current  strength  be- 
comes evaluated  in  c.  G.  s.  units  of  10  amperes  each. 

SYLLABUS. 

In  an  electric  circuit  the  current  strength  may  be  uni- 
form ;  in  a  dielectric  circuit  it  can  never  be  uniform. 

Conducting  circuits  may  be  series,  multiple,  multiple- 
series,  or  series-multiple. 


A  series  circuit  is  frequently  called  a  constant  current 
circuit.  In  such  a  circuit  the  current  is  usually  main- 
tained constant  even  though  the  resistance  be  variable. 

A  multiple  circuit  is  frequently  called  a  constant  po- 
tential circuit.  The  current  in  the  leads  is  variable,  but 
the  E.  M.  F.  is  constant. 

The  E.  M.  F.'S  developed  in  a  circuit  by  a  current  are 
all  counter  E.  M.  F.'S.  These  counter  E.  M.  F.'S  may  be 
divided  into  four  classes ;  viz.,  the  virtual  counter  E.  M.  F. 
of  resistance,  the  counter  E.  M.  F.  of  polarization,  the 
counter  E.  M.  F.  of  induction,  and  the  motor  electromotive 
force  of  a  motor. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 
WEEKLY. 

~NY>    Q  ArrnmsTll     1 KQ4-         Price,     -    10  Cents. 

11,  1    ^4.        Subscription,  $3.00. 

Electrical   Engineering  Leaflets, 


Prof.  E.-J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED     GF?ADE. 

VOLTAIC  CELL. 


61.  When  a  plate  of  chemically  pure  zinc  and  a 
plate  of  chemically  pure  copper  are  plunged  into 

a  dilute  solution  of  sulphuric  acid,  no  visible  action 
takes  place  as  long  as  the  plates  are  electrically  discon- 
nected outside  the  acid  liquid.  When,  however,  the 
two  plates  are  connected  outside  the  liquid  by  a  con- 
ducting wire,  the  completion  of  the  electric  circuit  is 
immediately  attended  by  the  establishment  of  an  elec- 
tric current  through  the  circuit,  and  a  more  or  less  visi- 
ble action  on  the  zinc,  as  evidenced  by  the  evolution  of 
hydrogen  and  the  gradual  solution  of  the  zinc  plate. 
Such  an  arrangement  forms  what  is  called  a  voltaic  cell. 

62.  The  electromotive  force   which  produces  the 
electric  current,  exists  at  the  contact  surfaces  of 

the  two  plates  with  the  liquid.  As  we  have  already 
seen,  whenever  an  E.  M.  F.  acts  in  the  direction  of  an 
electric  current,  energy  is  absorbed  from  the  source  of 
the  E.  M.  F.;  that  is,  work  is  done  on  the  current  and 

Published  by 

THE   ELECTRICAL  ENGINEER, 
203  Broadway,  New  York,  N.  Y. 

[Entered  as  second-class  matter  at  the  New  York,  N.  YM  Post  Office,  June  14,  1894.] 


66 


appears  in  the  circuit.  So  here,  when  an  E.  M.  r.  sets 
up  a  current  in  the  voltaic  circuit,  energy  is  absorbed  at 
the  source  of  the  E.  M.  r.;  namely,  at  the  junction  sur- 
faces between  the  plates  and  the  liquid  in  which  they 
are  immersed.  Such  a  combination  or  couple  of  two 
plates  or  elements,  with  the  conducting  solution  or  elec- 
trolyte is  called  a  voltaic  cell.  It  follows,  therefore, 
that  the  particular  combination  of  elements  and  electro- 
lyte in  a  voltaic  cell,  which  will  insure  the  most  powerful 
E.  M.  r.,  will  be  that  combination  which  will  ensure  the 
maximum  resultant  amount  of  work  being  absorbed  at  the 
immersed  surfaces  when  the  circuit  is  closed.  In  an  ac- 
tive voltaic  cell,  one  of  the  elements  or  plates  is  dissolved 
by  the  electrolyte  while  the  other  plate  remains  unat- 
tacked.  The  plate  which  is  dissolved  is  called  \\\v  posi- 
tive plate  of  the  couple  and  the  other  the  negative  plate. 
The  current  flows  through  the  liquid  from  the  posi- 
tive to  the  negative  plates,  as  shown  by  the  arrows, 
when  the  external  circuit  c  D  E  is  completed,  and  the 
terminal  c,  at  which  the  current  leaves  the  cell  is,  ac- 
cording to  convention,  called  the  positive  pole  or  terminal, 
and  the  terminal  z,  where  it  returns  to  the  cell,  the 
negative  pole  or  terminal.  It  will  be  seen,  therefore, 
that  the  negative  terminal  is  connected  with  the  positive 
plate,  and  the  positive  terminal  is  connected  with  the 
negative  plate.  This  classification,  although  generally 
used,  is  apt  to  mislead.  In  reality,  the  plate  A,  (allowing 
for  any  existing  drop  of  pressure)  must  have  the  same 
potential  throughout  its  substance ;  and,  similarly,  the 
plate  B,  must  be  positive  throughout.  Since  the  electro- 
motive force  is  resident  at  the  surface  of  contact  be- 
tween the  plates  and  the  liquid,  it  follows  that  the  entire 


67 


plate  B,  is  positive  to  the  liquid  and  the  entire  plate 'A, 
negative  to  the  liquid.  The  terms  positive  plate  and 
negative  plate,  however,  are  in  universal  use,  and  if 
properly  understood  introduce  no  error.  We  shall, 
therefore,  hereafter  employ  them. 

63.       It  has  frequently  been  stated  in  text-books  of  less 
recent  date  that  the  seat  of  the  E.  M.  r.,  for  ex- 
ample, the  zinc-copper  couple  shown  in  Fig.  24  is  at  the 


Vz         c/ 



| 

1 

0 

^ 

A           B 

3      ^_ 

CC      '', 
Ul      ' 

tt.     : 

Q.     : 

;     ^ 

8    ; 

\ 

5 

,;/% 

PIG,  24. — SIMPLE  FORM  OF  VOLTAIC  CELL. 

metallic  contact  of  the  zinc  plate  and  the  copper  wire 
outside  the  cell.  This  is,  however,  erroneous.  The  only 
E.  M.  F.  which  can  exist  at  this  metallic  junction  is  what  is 
called  a  thermo-electric  E.  M.  F.,  and  as  such  is  altogether 
two  small  to  account  for  the  E.  M.  F.  of  the  cell.  As 
has  already  been  pointed  out,  wherever  an  E.  M.  F.  aids 
or  opposes  a  current,  work  is  done  by  or  on  the  E.  M.  F. 
If,  therefore,  the  E.  M.  F.  of  the  voltaic  cell  resided  at 
the  zinc-copper  contact  outside  the  cell,  it  would  follow 


UHI7BRSIT7 


68 


that  the  energy  of  the  cell  would  be  supplied  at  this 
contact,  i.  e.  outside  the  cell,  and  would  therefore  be  in- 
dependent of  such  energy  relations  £s  existed  within  the 
cell.  In  point  of  fact,  however,  the  energy  is  absorbed, 
not  at  this  contact,  but  at  the  contact  surfaces  of  the 
plates  with  the  electrolyte,  and  it  is  to  these  surfaces, 
therefore,  that  we  have  to  look  for  the  E.  M.  F.  of  the  cell. 

64.  In   every   voltaic   cell   there  are  two   distinct 
sources  of  E.  M.  F.,  viz : 

(1.)  An  E.  M.  F.  at  the  contact  surface  of  the  positive 
plate  with  the  liquid. 

(2.)  An  E.  M.  F.  at  the  contact  surface  of  the  negative 
plate  with  the  liquid. 

When  a  cell,  such  as  shown  in  Fig.  24,  has  a  positive 
plate  of  zinc,  a  negative  plate  of  copper,  and  an  elec- 
trolyte of  dilute  sulphuric  acid,  on  the  closing  of  the 
circuit  hydrogen  sulphate,  Jf2  SO^  in  the  electrolyte  is 
decomposed.  The  negative  radical,  (SO^)  enters  into  com- 
bination with  the  zinc,  to  form  zinc  sulphate,  ZnSO^  and 
the  hydrogen  radical  H^  is  liberated  at  the  negative 
plate  in  the  form  of  bubbles  of  gas.  Before  closing  the 
voltaic  circuit,  we  have  a  condition  of  affairs  in  the  cell 
represented  by  the  chemical  expression 

Zm,  +  //2  SO  i  +  On, 
and  after  closing,  Zn/SO^  -f-  H2  +  Cu. 

65.  The  most  economical  voltaic  cell  that  has  been 
yet  developed,  is  incapable  of  producing,  on  a  large 

scale,  electric  energy  as  cheaply  as  a  dynamo  electric 
machine.  A  careful  consideration  will  show  how  hope- 
less it  is  to  expect  any  existing  voltaic  cell  economically 
to  compete  with  an  efficient  dynamo.  As  we  have 


already  pointed  out,  the  source  of  energy  in  the  cell  is 
the  chemical  potential  energy  in  the  positive  plate  and 
electrolyte.  For  example,  taking  for  the  positive  ele- 
ment the  metal  which  experience  has  shown  to  be  the 
most  economical  and  suitable,  namely  zinc,  one  pound  of 
zinc,  of  the  requisite  degree  of  purity,  costs,  when  made 
up  in  large  quantities  into  plates,  say  $0.07.  This  pound 
of  zinc  dissolved  in  a  voltaic  cell  without  loss  by  local 
action,  produces  a  delivery  of  about  1,347,500  coulombs, 
and  if  the  E.  M.  F,  of  the  cell  be  two  volts,  2,695,000  volt- 
coulombs,  i.  e.y  2,695,000  joules  of  electrical  energy, 
equal  to  0.7486  kilowatt-  hours,  so  that,  leaving  out  of 
consideration  the  cost  of  the  electrolytes  employed  in  the 
battery,  as  well  as  labor,  interest  and  depreciation,  the 
cost  of  a  kilowatt-hour  in  zinc  consumed,  is  9.352  cents 
per  kilowatt-hour  in  the  battery  circuit.  On  the  other 
hand,  it  is  known  that  1.8  Ibs.  of  coal  in  the  best  large 
steam  plants  will  furnish  one  average  indicated  horse- 
power-hour ;  or  2.4  Ibs.  of  coal,  one  average  indicated 
kilowatt-hour,  which  with  an  efficiency  of  conversion  in 
dynamo  machines  of  0.9,  represents  an  expenditure  of 
2f  Ibs.  coal  per  kilowatt-hour  of  electrical  energy  in  the 
dynamo  circuit.  With  coal  costing  $3.00  per  ton  of 
2,240  Ibs.,  the  cost  of  a  kilowatt-hour  is  thus  approxi- 
mately 0.357  cent  for  coal  consumed,  leaving  out  of 
consideration  water,  oil,  waste,  labor,  interest  and  depre- 
ciation. In  a  large  steam  dynamo  central  station,  the 
total  cost  of  producing  and  delivering  a  kilowatt-hour 
over  a  long  line  to  consumers  is  sometimes  seven  cents. 

66.       If  the  working  E.  M.  r.  of  a  cell  be  denoted  by 
e  (volts)  and  its  internal  resistance  by  r  (ohms) 

then  —  may  be  called  the  electrical  capability  of  the 


cell,  and  is  equal  to  the  activity  of  tlie  cell,  when  short 
circuited,  expressed  in  watts.  If  now  an  activity  of  P 
watts  is  required  from  the  battery  in  its  external  circuit,  the 
minimum  number  of  cells  which  will  supply  this  activity 

is4.P-^( —  J.     This  number  of   cells  will,  therefore, 

represent  the  most  economical  installation  or  first  cost. 

Thus  if  a  given  type  of  cell  has  an  E.  M.  F.  of  2  volts, 
and  a  resistance  of  0.1  ohm,  its  electrical  capability  is  40 
watts.  If  a  battery  of  these  cells  has  to  yield  160  watts 
in  its  external  circuit,  the  minimum  number  of  cells  re- 
quired is  4  X  —  =  16.  Each  cell  will  yield  to  the 

circuit  20  watts,  or  one-half  of  its  capability,  and  will 
yield  to  the  external  circuit  10  watts  or  one-quarter  of 
its  capability.  In  other  words,  minimum  installation 
cost  requires  an  efficiency  of  0.5  from  the  battery,  and 
half  the  capability  of  each  cell. 

67.  When  the  requisite  number  of  cells  has  been 
determined  by  the  preceding  rule,  the  grouping 

of  the  cells  does  not  alter  their  activity.  In  the  case 
considered,  if  16  cells  be  operated  in  series  the  terminal 
E.  M.  F.  would  be  16  volts  and  the  current  10  amperes. 
If  the  battery  was  arranged  "in  2  rows  of  8  cells,  the 
terminal  E.  M.  F.  would  be  8  volts,  and  20  amperes, 
similarly  for  4  rows  of  4  cells,  8  rows  of  2,  or  16  rows 
of  1,  the  output  would  be  160  watts.  The  grouping 
adopted  would  in  practice  depend  upon  the  nature  of 
the  receptive  device ;  i.  e.  the  motor  or  lamp  operated. 

68.  It  sometimes  happens  that  the  activity  required 
from  a  cell  for  minimum  installation  cost,  namely 

one-half  of   its  capability,  is  greater  than  the  cell  can 


71 


sustain.  In  such  cases  the  rule  must  be  modified.  If 
'*,  be  the  maximum  current  strength  in  amperes  which 
the  cell  can  sustain,  then  e  i,  is  its  maximum  yield  to  the 
circuit,  and  e  i  —  i*  r,  its  maximum  delivery  to  the  ex- 
ternal circuit.  Hence  if  JP,  be  the  external  activity  re- 
quired, the  minimum  number  of  cells  which  will  yield 

it  is     .        .,     . 

e  ^  —  v*  r 

For  example,  in  the  cells  already  considered,  the 
theoretical  current  obtainable  from  them  on  short-cir- 
cuit would  be  ¥2T  —  20  amperes  and  the  most  economical 
working  current  in  regard  to  first  cost  of  battery  would 
be  ten  amperes.  But  if  the  maximum  current  practi- 
cally obtainable  from  these  cells  without  undue  polari- 
zation was  four  amperes,  then  the  minimum  number 
required  to  yield  160  watts  in  the  external  circuit  would 


be  -  -  —  -  =  25,  and  this  might  be  arranged  in  one, 
8  —  1.6 

or  five  rows,  according  to  requirements.  The  efficiency 
of  the  battery  would  no  longer  be  0.5.  In  this  instance 
it  would  be  0.8. 

69.  It  should  be  observed  that  in  order  to  obtain 
the  best  economy  in  operating  and  maintaining  a 
battery  for  a  given  activity,  the  cost  of  materials  and 
superintendence  have  to  be  considered  as  well  as  interest, 
depreciation,  and  first  cost,  so  that  the  number  of  cells 
for  best  working  economy,  may  be  very  different  from 
the  number  of  cells  for  lowest  first  cost  of  installation. 

TO.       The  value  of  any  type  of  cell,  in  regard  to  the 

minimum  number  that  must  be  installed  for  the 

supply  of  a  given  power  is  proportional  to  its  capability, 


72 


and  if  p,  be  the  price  in  dollars  of  any  given  type  of  cell,  its 
economic  value  for  cost  of  installation  is  proportional  to 

<> 

Thus,  two  cells  would  have  equal  economic  value 

p  r 

for  the  delivery  of  a  small  quantity  of  power,  reckoned 
on  the  basis  of  first  cost  in  installation,  if  one  had  two 
volts  0.1  ohm,  and  cost  $1.00 ;  while  the  other  had  0.6 
volt,  0.012  ohm  and  cost  $0.75. 

71.  "Whenever  in  order  to  secure  the  maximum  first 
cost  of  battery  by  obtaining  an  efficiency  of  0.5, 
the  cells  of  a  battery  have  to  be  joined  up  in  multiple 
series,  it  is  preferable  to  employ  larger  cells  in  a  single 
series  if  possible.  Such  a  proceeding  is  not  only  more 
economical,  since  large  cells  cost  relatively  less  than 
smaller  ones,  but  will  also  be  a  safegard  against  defec- 
tive action  by  the  failure  of  cells  in  any  series,  thereby 
allowing  the  neighboring  series  to  discharge  through  it 
thus  seriously  interfering  with  the  effectiveness  of  the 
battery. 

SYLLABUS. 

The  seat  of  E.  M.  F.  in  a  voltaic  cell  is  at  the  contact 
surfaces  of  the  plates  or  elements  of  the  voltaic  couple 
with  the  electrolyte  or  electrolytes. 

It  is  erroneous  to  ascribe  the  seat  of  E.  M.  F.  in  a  vol- 
taic cell  to  the  metallic  junction  outside  the  cell. 

In  any  cell,  the  ratio  of  the  square  of  the  E.  M.  F.  to 
the  resistance,  may  be  called  the  capability  of  the  cell. 

The  economic  value  of  a  cell,  so  far  as  regards  first 
cost,  is  its  capability  divided  by  its  price. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 
WEEKLY. 

No    10  Arrrnvr  1$    1 SQ4-          Price>     '     10  Ccuts- 

lb,  1    M.        Subscription,  $3.00. 

Electrical    Engineering   Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED     GRADE. 

THE    VOLTAIC  CELL. 


72.  The  conduction  of  an  electric  current  by  an 
electrolyte  is  of  a  different  nature  from  the  con- 
duction afforded  by  metals.  In  the  latter  case,  apart 
from  an  elevation  of  temperature,  the  passage  of  the 
current  is  attended  by  no  change  in  the  metal.  In  the 
case  of  an  electrolyte,  however,  the  passage  of  an  elec- 
tric current  is  invariably  attended  by  a  decomposition  or 
dissociation  of  some  of  the  constituent  molecules.  This  is 
accounted  for  on  the  supposition,  that  in  liquids,  only  the 
ions,  i.e.,  the  dissociated  molecules,  are  capable  of  carry- 
ing an  electric  current,  and,  if  no  dissociated  molecules 
existed  in  the  solution,  that  solution  would  act  as  an  in- 
sulator. The  action  of  an  E.  M.  F.  on  an  electrolyte  is, 
therefore,  to  direct  the  movement  of  the  ions. 

Since  atoms  possess  definite  electric  capacity,  differing 
for  different  kinds  of  atoms,  but  always  the  same  for  the 
same  kind  of  atom,  it  follows  that  the  passage  of  a  definite 
quantity  of  electricity,  say  one  coulomb,  must  necessitate 

Published  by 

THE   ELECTRICAL   ENGINEER, 
203  Broadway,  New  York,  N.  Y. 

[Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  June  14,  1894.] 


the  transfer  of  a  definite  number  of  atoms  or  radicals, 
different  in  the  case  of  hydrogen  than  in  that  of  oxygen; 
consequently  a  definite  quantity  or  mass  of  any  given  radi- 

TABLE  OF  ELECTRO-CHEMICAL  EQUIVALENTS. 


Element. 

Atomic  Weight. 

&*» 
o 

c 

1 

Electro  -chemi- 
cal Equival- 
ents. Milli- 
grammes per 
Coulomb. 

Coulombs  per 
Gramme. 

B* 
l| 
kl 

H 

•^ 

Hydrogen         

1 

1 

0  01038 

96340 

12140 

Potassium  

39  03 

1 

0  4051 

2469 

311  1 

Sodium  

23.0U 

1 

0  2387 

4189 

527  8 

Silver    

1U7.7 

1 

1.118 

894  5 

112  7' 

Copper,  in  cuprous  combina- 
tions   

63  18 

1 

0  6558 

1525 

192  1 

Mercury,  in  mercurous  com- 
binations 

199  8 

1 

2  074 

482  2 

60  75 

Chlorine  ... 

35  37 

1 

0  3671 

2724 

343  2 

Iodine  .... 

126  54 

1 

1  3134 

761  4 

95  93 

Bromine  

79  76 

1 

U  8279 

1208 

1522 

Copper,  in   cupric  combina- 
tions   
Mercury,   in  mercuric  com- 
binations   
Tin,  in    stannous    combina- 
tions            

63.18 
199.8 
117.4 

2 
2 

9, 

0.3279 
1.037 
0.6093 

3050. 
964.3 
1641 

384.3 
121.5 
2068 

Iron,  in  ferrous  combinations 
Nickel  

55.88 
58.6 

2 
2 

0.2900 
0.3042 

3448. 

3287. 

434.4 
414.1 

Zinc      .       

64.88 

9, 

0  3367 

2970 

374.2 

Lead  

2U6.4 

2 

1  071 

933.7 

117.6 

Oxygen  .  . 

15.96 

2 

0.08283 

12070. 

1521. 

Gold      

196  2 

g 

0.6789 

1473 

185  6 

Iron,  in  ferric  combinations. 
Aluminum  

55.88 
27.04 

3 
3 

0.1934 
0.0935 

5171. 
10700. 

651.5 
1348. 

Nitrogen  
Tin,  in  stannic  combinations 

14.U1 
117.4 

3 

4 

0.04847 
0.3046 

20630. 
3283. 

2599. 
413.6 

cal  is  invariably  dissociated  and  transferred  by  the 
passage  of  one  coulomb  of  electricity.  This  mass  ex- 
pressed in  grammes  is  called  the  electro-chemical  equiv- 


75 


alent  of  the  radical.  For  example,  one  coulomb  of 
electricity  passing  through  an  electrolyte  will  transfer 
0.00001038  gramme  of  hydrogen. 

A  table  of  electro-chemical  equivalents  is  given  on 
page  74, 

73.  It  will  be  seen  from  the  table  that  the  electro- 
chemical equivalent  of  silver  is  1.118  milli- 
grammes ;  therefore,  each  coulomb  of  electricity  will 
liberate  1.118  milligrammes  of  silver,  and  each  ampere- 
hour  will  liberate  3600  X  Vwo  =  4.0248  grammes  of 
silver. 

It  will  also  be  observed  that  the  electro-chemical 
equivalent  of  any  monad  element,  such  as  hydrogen, 
chlorine,  nitrogen,  iodine,  etc.,  is  directly  proportional  to 
its  atomic  weight.  Thus  the  electro-chemical  equivalent 
of  chlorine  is  35.37  times  the  electro-chemical  equivalent 
of  hydrogen.  This  is  tantamount  to  the  statement  that 
all  monad  atoms  or  radicals  carry  the  same  electric  charge; 
that  all  dyad  atoms  or  radicals  carry  twice  the  charge  of 
a  monad  atom  ;  that  all  triad  atoms  or  radicals  carry 
three  times  the  charge  of  a  monad  atom ;  that  all  tetrad 
atoms  or  radicals  carry  four  times  the  charge  of  a  monad 
atom.  Consequently,  when  an  electric  current  passes  in 
series  through  solutions  of  various  chemical  substances, 
there  will  be  liberated  one-fourth  as  many  tetrad,  one- 
third  as  many  triad,  and  one-half  as  many  dyad,  as  monad 
atoms  or  radicals. 

Thus,  one  coulomb  of  electricity  will  liberate 
0.00001038  X  ^y-8  grammes  of  copper  from  cupric 
solutions,  for  the  reason  that  the  atomic  weight  of  cop- 
per is  63.18,  and  copper,  in  such  salts,  is  a  dyad  radical. 


76 


Generally,  in  the  case  of  any  element  or  radical,  the 
mass  in  grammes  liberated  by  one  coulomb  is, 

0.00001038  X  ~'™  Weij;ht 

valency 

74.  Whenever  a  definite  chemical  combination  oc- 
curs, a  certain  amount  of  energy  is  either  ab- 
sorbed or  liberated.  In  the  case  of  the  mere  chemical 
formation  of  zinc  sulphate  from  metallic  zinc  and  sul- 
phuric acid,  energy  is  liberated  as  heat.  If,  however, 
the  same  combination  is  effected  in  a  voltaic  cell,  when 
the  circuit  is  closed,  this  energy  is  no  longer  liberated  as 
heat,  but  as  electric  energy,  and  the  same  number  of 
joules  appear  in  the  circuit  as  before.  It  is  evident, 
therefore,  that  the  E.  M.  F.  is  capable  of  being  calcu- 
lated when  the  thermo-chemical  equivalents  of  its  forma- 
tion products  are  known. 

By  the  thermo-chemical  equivalent  of  a  substance  is 
meant  the  amount  of  energy  liberated  by  the  chemical 
combination  of  its  molecular  weight  with  any  other  sub- 
stance. This  energy  is  usually  expressed  in  gramme- 
calories,  i.  <?.,  the  amount  of  heat  necessary  to  raise  the 
temperature  of  one  gramme  of  water  1°  C.,  but  may  be 
expressed  in  joules. 

Suppose  that  exactly  one  coulomb  of  electricity  flows 
through  a  circuit  from  a  Daniell  cell.  There  will  be 
0.00001038  X  Mj-8-8  =  0.0003367  grammes  of  zinc  dis- 
solved and  converted  into  zinc  sulphate.  There  will  also 
be  0.00001038  X  4y^  =  0.0003279  grammes  of  copper 
deposited  on  the  negative  plate. 

Heat  is  evolved  by  the  normal  formation  of  zinc-sul- 
phate from  zinc,  and,  one  gramme  of  zinc,  converted 
into  ZnSOt  and  dissolved  in  water,  is  known  by  experi- 


77 


ment  to  yield  16,090  joules  of  energy  in  the  form  of 
heat,  so  that  0.0003367  gramme  of  zinc  dissolved  by 
ordinary  chemical  processes  would  yield  5.417  joules. 

But,  on  the  other  hand,  work  requires  to  be  expended 
in  order  to  reduce  copper  from  a  solution  of  copper 
sulphate,  and  it  has  also  been  found  by  measurement 
that  the  energy  necessary  to  resolve  one  gramme  of  cop- 
per in  this  manner  is  13,190  joules,  or  to  resolve 
0.0003279  gramme,  4.324  joules.  Thus  for  every 
coulomb  of  electricity  generated  by  the  cell,  chemical 
changes  are  effected  within  it  which  would  represent 
5.417  joules  produced  at  the  positive  plate,  and  4.324 
joules  expended  at  the  negative  plate,  leaving  a  balance 
of  1.093  joules  developed  in  the  cell. 

If  the  chemical  changes  occurred  under  chemical 
action  alone,  the  1.093  joules  would  be  expended  in 
heating  the  contents  of  the  cell,  just  as  water  is  heated 
by  the  admixture  of  sulphuric  acid.  As,  however,  the 
changes  occur  under  electrical  action,  the  1.093  joules  do 
not  appear  as  heat  in  the  cell,  but  in  the  entire  circuit  as 
electrical  energy,  of  the  type  E  q,  (see  Paragraph  15),  and 
since  E  q  =  1.093  joules,  and  q  is  here  chosen  as  unity, 
we  have  E  —  1.093  volts. 

75.  According  to  the  principles  of  the  conservation 
of  energy  we  have  thus  determined  that  the 
E.  M.  F.  of  the  Daniell  cell  must  be  1.093  volts,  in  order 
that  the  energy  accompanying  the  chemical  changes  in 
the  cell  should  be  wholly  developed  in  the  circuit,  and 
assuming  that  the  experimentally  determined  energy 
valuations  of  these  chemical  changes,  i.e.,  their  thermo- 
chemical  equivalents,  have  been  accurately  measured. 

In   fact,   1.09  volts  is  very  nearly  the  E.  M.  F.  of  a 


78 


Daniell  cell  freshly  set  up,  with  pure  metal  plates,  and 
pure  saturated  solutions.  In  practice,  owing  to  a  variety 
of  causes,  the  E.  M.  F.  is  usually  lower  than  this,  and,  on 
closed  circuit  work,  may  even  be  below  one  volt. 

We  have  remarked  that  the  E.  M.  r.  was  calculated  on 
the  assumption  that  the  chemical  energy  developed  in 
the  cell  was  not  liberated  there  as  heat.  Practically, 
however,  some  heat  is  generated  in  the  cell  during  its 
electric  activity.  This  is  only  a  secondary  consequence 
of  the  electric  resistance  of  the  cell ;  and  its  share  of 
the  total  resistance  in  the  circuit,  determines  the  propor- 
tion of  heat  that  will  be  developed  within  the  cell.  If 
the  cell  be  so  constructed  as  to  offer  a  negligibly  small 
resistance,  then  the  amount  of  heat  electrically  devel- 
oped by  the  current  would  be  negligibly  small,  and  all 
the  chemical  energy  developed  by  chemical  changes  in 
the  cell  would  be  liberated  outside  the  cell,  i.e.,  in  the 
external  circuit,  by  the  electric  agencies. 

It  should  be  remarked,  however,  that  owing  to  the 
incompleteness  of  our  knowledge  of  thermo-chemical 
equivalents,  and  of  the  exact  nature  of  the  electro-chemi- 
cal actions  in  the  cell,  the  E.  M.  F.  of  a  cell  can  in  only  a 
few  instances  be  practically  predetermined. 

A  voltaic  cell  is,  therefore,  a  device  for  liberating 
outside  the  cell  the  energy  developed  by  its  chemical 
activities,  and  if  the  amount  of  those  chemical  activities 
is  completely  known,  the  E.  M.  F.  of  the  cell  is  deter- 
minate by  purely  thermo-chemical  measurements. 

Irrespective  of  the  cost  of  materials,  the  best  type  of 
cell  would  be  one  in  which  the  thermo-chemical  energy 
developed  in  the  changes  effected  at  the  positive  plate 
would  be  a  maximum,  and  in  which  the  expenditure  of 


79 


thermochemical  energy  developed  in'  the  changes  effected 
at  the  negative  plate  would  be  a  minimum.  Such  a  cell 
would  possess  the  maximum  E.  M.  F. 

76.  From  the  hundreds  of  combinations  that  have 
been  tried,  the  zinc-carbon  chromic  acid  type  of 
cell  appears  to  possess  the  greatest  E.  M.  F.  practically 
available  ;  viz.,  about  two  volts. 

The  disadvantage  of  this  cell,  however,  lies  in  the 
fact,  that  since  the  chromic  acid  around  the  negative 
plate  freely  attacks  zinc,  it  is  necessary  to  employ  a 
porous  jar  to  contain  it,  and  even  this  resource  only  re- 
tards diffusion  and  causes  waste  of  zinc  on  open  circuit, 
besides  adding  considerably  to  the  resistance  of  the  cell. 

SYLLABUS. 

In  metallic  conduction  no  visible  change  in  the  con- 
ducting circuit  is  produced  beyond  a  change  in  its  tem- 
perature. 

In  electrolytic  conduction  the  passage  of  the  current 
is  invariably  attended  by  the  dissociation  of  some  of  the 
constituent  molecules  of  the  liquid  conductor,  i.e.,  of 
its  electrolyte. 

The  electrical  capacity  of  the  ultimate  atoms  of  matter 
differs  for  different  kinds  of  atom,  but  is  invariably  the 
same  for  the  same  kind  of  atoms. 

In  electrolytic  conduction  the  passage  of  one  coulomb 
of  electricity  necessitates  the  transfer  of  a  number  of 
atoms  or  radicals  dependent  on  their  electro-chemical 
equivalents. 

The  electric  carrying  capacity,  or  charge,  of  all  monad 
atoms  is  the  same.  The  charge  of  all  dyad  atoms  is 


80 


twice,  of  all  triad  atoms  three  times,  and  of  all  tetrad 
atoms  four  times  that  of  a  monad  atom ;  consequently, 
the  electro-chemical  equivalent  of  an  atom  of  any  element 
will  be  proportional  to  its  atomic  weight  divided  by  its 
valency. 

•  The  E.  M.  F.  produced  by  any  voltaic  cell  may  be  cal- 
culated when  the  thermo-chemical  equivalents  of  its 
formation  products  are  known,  and  is  equal  to  the  total 
resulting  joules  developed  in  the  cell  by  its  chemical 
action,  per  coulomb  of  electricity  passing  through  it. 

In  every  voltaic  cell  thermo-chemical  energy  is  liber- 
ated at  the  positive  plate  and  absorbed  at  the  negative 
plate.  The  maximum  E.  M.  F.  will,  therefore,  be  pro- 
duced when  the  former  action  is  greater  than  the  latter. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 
WEEKLY. 

NY>    11  AiTnn«iT  9^    1SQ4-         Price,     -    10  Cents. 

1  J0,  1    M.         Subscription,  $3.00. 

Electrical    Engineering   Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED     GRADE. 

THE   VOLTAIC  CKLL 


77.  The   hydrogen   evolved  at  the  surface  of  the 
negative  plate  adheres  to  the  plate,  and  produces 

by  its  contact  an  electromotive  force,  counter  or  opposed 
to  that  of  the  cell.  This  is  called  the  counter  E.  M.  F. 
of  polarization.  Various  methods  are  employed  to  pre- 
vent polarization.  These  consist,  practically,  of  methods 
by  which  the  hydrogen  is  either  prevented  from  being 
evolved  at  the  negative  plate  ;  or,  if  evolved,  prevented 
from  forming  there  by  entering  into  combination  with 
some  suitable  substance  surrounding  the  negative  plate. 
This  substance  is  called  a  depolarizer. 

78.  Voltaic  cells  may  be  divided  into  the  following 
classes  according  to  the  presence  or  absence  of 

a  depolarizer  and  its  character,  viz. : 

(1.)  Single-fluid  cells  or  those  which  possess  an  excit- 
ing fluid  but  no  depolarizer. 

(2.)  Single-fluid  cells  with  solid  depolarizers  surround- 
ing, or  in  contact  with,  the  negative  plate. 

Published  by 

THE'  ELECTRICAL   ENGINEER, 
203  Broadway,  New  York    N.  Y. 

[Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  June  14   1894.] 


82 


(3.)  Double-fluid  cells,  or  those  with  an  exciting  fluid 
and  a  fluid  depolarizer. 

79.  In  single-fluid  cells  no  steps  are  taken  to  avoid 
polarization.      It  is  evident,  therefore,  that  the 

cells  cannot  be  successfully  employed  for  furnishing  a 
continued  electric  current.  Indeed,  even  for  temporary 
currents,  they  are  inferior  to  most  forms  of  efficient  cells 
with  depolarizers. 

One  of  the  earliest  forms  of  single-fluid  cell  was  the 
Smee  cell,  a  zinc-silver  couple,  immersed  in  an  electro- 
lyte of  dilute  sulphuric  acid  in  water.  This  cell  was  at 
one  time  largely  used  in  telegraphy  and  in  electroplating. 
It  has  now  almost  entirely  disappeared,  being  replaced 
by  more  efficient  types  of  cell,  or  by  dynamo  electric 
machines. 

80.  A  form  of  single-fluid  (fell,  which  is  still  em- 
ployed for  producing  powerful  currents  for  brief 

intervals  of  time,  is  the  zinc-carbon  couple  immersed  in 
a  solution  of  sal-ammoniac  in  water. 

Like  all  cells  of  the  single-fluid  type  without  depolar- 
izers, this  cell  requires  long  intervals  of  rest  in  order  to 
regain  its  full  E.  M.  F. 

81.  The  Grenet,  the  bichromate,  or  the  Poggendorf 
cell,  as  it  is  indifferently  called,  consists  of  a  zinc- 
carbon  couple  immersed  in  an  electrolyte  of  bichromate  of 
potash  and  sulphuric  acid.    The  reactions  occuring  in  this 
cell,  when  at  work,  are  probably  represented  as  follows : 

Before  action, 

3  Zm,  +  7  H2  SO,  +  ^2  Or.,  0,  +  C. 
After  action, 
3  ZnSOi  +  7  ff2  O  +  KI  SO \  +  Or*  (SO^  +  C. 


In  the  Grenet  cell,  the  zinc  plate  should  be  removed 
from  the  electrolyte  when  not  in  use,  since  otherwise 
deleterious  local  action,  or  irregular  consumption  of  the 
zinc  will  occur.  For  this  purpose  some  arrangement  is 
generally  made  to  lift  either  the  zinc  only,  or  both  the 
zinc  and  carbon  from  the  liquid,  as  shown  in  Fig.  25, 
where  a  form  of  cell  suitable  for  use  in  driving  the  motor 
of  a  phonograph  is  illustrated.  Although  the  Grenet 
cell  may  be  regarded  as  a  single -fluid  cell  without  any 
separate  depolarizer,  yet,  in  point  of  fact,  the  exciting 


FIG.  25. — FORM  OF  GRENET  FIG.  26. — FORM  OP  GRAVITY 

CELL.  DANIELL  CELL. 

solution  acts  both  as  an  exciting  liquid  ai^d  as  a  depolar- 
izer, since  no  free  hydrogen  makes  its  appearance  at  the 
negative  plates.  Such  a  cell  as  is  represented  in  Fig.  25 
will  supply  three  amperes  steadily. 

82.       In   double-fluid  cells,  in  order  to  prevent  the 

depolarizing  liquid  from  mixing  with  the  exciting 

liquid,  the  depolarizing  liquid  is  generally  placed  in  a 

porous  jar.     The  presence  of  the  porous  jar  greatly  in- 


creases  the  internal  resistance  of  the  voltaic  cell  on  account 
of  the  high  resistivity  of  the  unglazed  earthenware  of  which 
it  is  formed. 

The  Daniell  cell  possesses  the  great  advantage  of  giving 
a  continuous,  steady  current,  provided  the  current  density 
in  the  cell  is  not  excessive. 

The  reaction  which  occurs  in  this  cell  is  probably  ex- 
pressed by  the  following  equation  : 

Before  action, 

2n  +  H2  80,  +  Cu  SO,  +  Gu. 

After  action, 

ZifiSO,  +  HI  SO,  +  Cu  +  Cu. 

83.  In  practice,  the  inconvenience  arising  from  the 
use  of  a  porous  jar,  led  Callaud  to  modify  the 
Daniell  cell  for  closed-circuit  work.  In  the  Callaud  cell 
the  porous  partition  is  entirely  dispensed  with,  and  the 
zinc  sulphate  and  copper  sulphate  solutions  are  separated 
entirely  by  reason  of  their  differences  of  density.  Fig.  26 
shows  the  Callaud  or  gravity  cell.  The  copper  element 
consists  of  a  sheet  of  copper,  bent  as  shown,  placed  at  the 
bottom  of  the  cell  and  provided  with  an  insulated  wire 
passing  out  at  the  top.  The  zinc  plate  has  generally  the 
form  of  a  star  or  crowfoot,  and  is  suspended  near  the  top  of 
the  jar.  After  the  battery  has  been  in  use  for  some  time, 
the  zinc  sulphate  formed  by  its  action,  will  be  seen  as  a 
clear  transparent  liquid  layer  separated  from  the  dense 
blue  copper  sulphate  solution,  in  the  lower  part  of  the 
jar,  by  a  sharply  marked  boundary.  After  the  cell  has 
been  in  use  some  time,  some  of  the  zinc  sulphate  solution 
requires  to  be  drawn  off,  a  handful  of  copper  sulphate 
crystals  thrown  in,  and  fresh  water  added.  A  film  of 


85 


oil  is  frequently  poured  on  the  liquid  so  as  to  avoid  the 
effects  of  creeping,  and  to  prevent  evaporation. 

The  ordinary  form  of  Callaud  cell  should  not  be  called 
upon  to  deliver  more  than  J  ampere  steadily.  Special 
forms  of  gravity  cell  are  sometimes  employed,  called 
Tray  cells,  which  will  supply  five  amperes  steadily. 

84.       Fig.  27  shows  the  Leclanche  cell,  which  has  a 

zinc-carbon  couple.     The  zinc  is  in  the  form  of  a 

rod.    The  carbon  is  placed  inside  a  porous  cell  and  closely 

packed  with  powdered  carbon  and  black  oxide  of  mangan- 


FIG.  27. — FORM  OF  LECLANCHE  CELL.    FIG.  28.  — PARTZ  GRAVITY  CELL. 

ese,  the  latter  acting  as  a  solid  depolarizer.  The  exciting 
liquid  is  a  solution  of  sal-ammoniac  in  water.  This  cell  is 
made  in  a  variety  of  forms.  In  one  form,  called  the 
agglomerate  form,  the  porous  cell  is  dispensed  with,  and 
the  crushed  carbon  and  manganese  dioxide  are  moulded 
around  the  carbon  plate  under  great  pressure. 

The  action  of  the  Leclanche  cell  is  probably  represented 
as  follows : 

Before  action, 

Zn  +  2  NEt  Cl  +  2  MnO2  +  C. 

After  action, 

2  NH*  +  M.NI  o,  +  zra  o  +  o. 


"When  the  cell  is  overworked,  the  reactions  that  take 
place  are  very  obscure. 

85.  Fig.  28  shows  a  Partz  acid  gravity  cell.  It  is 
com  posed  of  a  zinc-carbon  couple ;  the  carbon  plate 
rests  on  the  bottom  of  the  jar,  while  the  zinc  is  sus- 
pended near  the  top. 

On  charging,  the  jar  is  partly  filled  with  an  aqueous 
solution  of  common  salt  or  of  sulphate  of  magnesia.  A 
specially  prepared  salt,  consisting  of  a  mixture  of  chromic 
and  sulphuric  acids  is  now  added  through  the  funnel 


FIG.  29. — FULLER  CELL 


FIG.  30. — EDISON-LALANDE  CELL. 


tube  shown  at  the  side.  This  salt,  on  reaching  the  bot- 
tom of  the  cell,  dissolves  and  spreads  over  the  surface  of 
the  carbon  plate  and  acts  as  a  depolarizer.  Its  greater 
density  keeps  it  at  the  bottom  of  the  vessel. 

86.  Fig.  29  shows  a  Fuller  mercury  bichromate  cell, 
which  consists  of  a  zinc-carbon  couple  with  the 
carbon  immersed  in  an  electrolyte,  consisting  of  a  solu- 
tion of  bichromate  of  potash,  sulphuric  acid  and  water,  and 
the  zinc,  which  is  usually  in  the  form  of  a  truncated 
cone,  placed  inside  a  porous  cell  filled  with  dilute  sul- 
phuric acid  in  water.  A  small  quantity  of  mercury  is 


8Y 


poured  into  the  porous  cell  to  thciuughly  amalgamate 
the  zinc.  This  cell  gives  a  high  electromotive  force  and 
a  fairly  steady  current,  but  possesses  the  disadvantage 
attending  all  cells  with  porous  partitions  of  a  compara- 
tively high  internal  resistance,  and  waste  of  chemicals  on 
open  circuit. 

87.  Fig.  30   shows  an  Edison-Lalande   cell,  which 
consists  of  a  zinc-copper  couple  in  a  solution  of 

caustic  soda  in  water.  A  solid  depolarizer  is  used  in 
this  cell  consisting  of  a  block  of  black  oxide  of  copper 
supported  in  a  frame  or  grid  of  copper.  The  action 
consists  in  the  formation  of  a  zincate  of  soda,  and  the 
reduction  of  the  copper  oxide  to  metallic  copper  on  the 
external  surface  of  the  block.  Owing  to  the  fact  that 
the  zinc  and  copper  plates  have  large  surfaces  placed  in 
close  proximity  to  each  other,  the  internal  resistance  of 
this  cell  13  remarkably  low,  and  forms  the  nearest  ap- 
proach, on  the  part  of  a  primary  battery,  to  the  internal 
resistance  of  a  storage  cell.  For  this  reason  it  is  capable 
of  supplying  strong  currents,  although  its  E.  M.  r.  is 
comparatively  low  (-§-  volt).  Its  local  action  is  usually 
negligible. 

88.  The  chloride  of  silver  cell  consists  of  a  zinc-silver 
couple  immersed  in  a  solution  of  sal-ammoniac  in 

water.  The  depolarizer  is  a  mass  of  chloride  of  silver 
fused  as  a  rod  around  a  silver  wire.  The  electromotive 
force  of  this  cell  is  very  uniform,  but  owing  to  the  ex- 
pense of  silver  plates  these  can  not  be  given  a  large  sur- 
face, and  hence  the  cells  possess  a  comparatively  high 
internal  resistance  and  are  unsuited  to  the  delivery  of 
strong  currents.  For  testing  purposes,  however,  the 


88 


portability  and  constancy  of  the  cell  renders  its  use 
admirable,  and  it  is  frequently  made  up  into  portable 
batteries,  one  of  which  is  shown  in  Fig.  31. 

89.       Fig.  32  shows  two  of  Clark's  standard  cells  en- 
closed in  a  brass  box  with  a  hard  rubber  cover  and 
a  thermometer  suitably  placed  to  indicate  the  tempera- 
ture of  the  interior. 


FIG.  31. — BATTERY  OF  SILVER  CHLOR-  FIG.  32. — PAIROF<JLAKK  STAND- 
IDE  CELLS  IN  SERIES.  ARD  CELL^  ENCLOSED  IN  A 

CASE  WITH  A  THERMOMETER. 

SYLLABUS. 

Yoltaic  cells  are  of  three  general  classes,  viz. :  single- 
fluid  cells  with  an  exciting  liquid  and  no  depolarizer; 
single-fluid  cells  with  an  exciting  liquid  and  a  solid  depo- 
larizer, and  double-fluid  cells  with  both  an  exciting 
liquid  and  a  liquid  depolarizer. 

Voltaic  cells  without  depolarizers  are  generally  un- 
serviceable. 

Voltaic  cells  with  solid  depolarizers  have  come  into 
very  extended  use. 

Laboratory  of  Houston  &  Kennelly, 
'Philadelphia, 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 
WEEKLY. 

No.  12.  SEPTEMBER  1,  1894. 

Electrical    Engineering   Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED 

\4asnetomotive  Korce 


90.  The  space  surrounding  a  magnet,  known  tech- 
nically as  a  magnetic  field,  is  a  region  trav- 
ersed or  permeated  by  magnetic  flux.  Although  the 
physical  nature  of  magnetic  flux  is  unknown,  yet  it 
possesses  both  magnitude  and  direction,  and  its  presence 
is  accompanied  by  a  condition  of  stress  in  the  ether.  It 
is  assumed  that  the  direction  of  magnetic  flux  is  such 
that  it  issues  from  the  positive  or  north-seeking  pole  of 
a  magnet,  commonly  called  the  north  pole,  and,  after 
passing  through  the  region  outside  the  magnet,  re-enters 
it  at  its  negative  or  south-seeking  pole,  completing  the 
circuit  through  the  substance  of  the  magnet.  The  direc- 
tion of  the  flux,  at  any  point  of  a  path,  is  that  which 
would  be  assumed,  at  that  point,  by  the  magnetic  axis  of 
a  freely  suspended  small  magnetic  needle.  The  strength 
of  this  magnetic  flux  rapidly  diminishes  with  the  distance 
from  the  magnet. 

Published  by 

THE   ELECTRICAL  ENGINEER, 
203  Broadway,  New  York   N.  Y. 

[Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  June  14,  1894.! 


90 


91.  Outside  the  magnet  the  magnetic  flux  is  strong- 
est in  the  neighborhood  of  the  poles,  where  its 

density  is  said  to  be  a  maximum.  The  unit  of  magnetic 
flux  is  called  the  weber.  Flux-density,  or  flux  intensity, 
is  defined  as  being  the  quantity  of  flux  passing  through 
a  normal  or  perpendicular  square  centimetre  of  area,  so 
that  unit  flux-density  is  a  flux  of  one  weber  through  a 
normal  square  centimetre,  and  is  called  a  gauss.  Flux- 
density  is  usually  represented  by  the  symbol  (B.  In  the 
open  country,  in  the  neighborhood  of  New  York,  the 
flux-density  of  the  earth's  magnetic  field  is  about  0.0  gauss, 
directed  downwards  at  an  inclination  of  about  72°. 
Although  the  flux-density,  in  the  space  outside  a  magnet, 
is  greatest  in  the  neighborhood  of  its  poles,  yet,  in  the 
case  of  a  homogeneous  magnet,  the  flux-density  in  the 
magnetic  circuit  is  usually  greatest  at  some  point  within 
the  magnet. 

92.  If  the  distribution  of  magnetic  flux  outside  along 
cylindrical  bar  magnet  be  mapped  out  by  the  aid 

of  a  small  magnetic  needle,  it  will  be  found  that  the  flux- 
paths  are  similar  in  direction  and  magnitude  to  the 
stream-lines  which  would  exist  in  an  incompressible  fluid 
surrounding  the  magnet,  if  this  were  a  hollow  tube  con- 
taining a  force  pump  so  operated  that  the  fluid  was  con- 
tinually being  forced  out  at  one  end  and  in  at  the  other. 

93.  A  magnetic  flux  differs  from  any  material  flux 
with  which  we  are  acquainted,  in  that  while  it  is 

associated  with  energy,  since  in  all  cases  it  requires  an 
expenditure  of  energy  to  establish  it,  yet,  it  requires 
no  expenditure  of  energy  to  maintain  its  existence  after 
it  has  been  once  established.  The  amount  of  energy 


91 


stored  up  in  magnetic  flux  is  represented  by  H-J  ergs  per 

cubic  centimetre  of  air  or  other  non-magnetic  material, 
so  that  the  amount  of  energy  existing  in  a  cubic  centi- 
metre of  air,  in  the  neighborhood  of  New  York,  owing 
to  the  existence  of  the  earth's  magnetic  flux,  is  about 


A  marked  difference  exists  in  this  respect  between  the 
electric  and  magnetic  circuit,  since,  in  the  electric  circuit, 
a  constant  expenditure  of  energy  to  the  amount  of  $  p 
ergs  per  cubic  centimetre  —  where  *',  is  the  current  density, 
and  p,  the  resistivity  of  the  material  in  the  circuit  —  has  to 
be  maintained  as  long  as  the  current  is  flowing  ;  whereas, 
in  the  magnetic  circuit,  no  energy  is  required  to  maintain 
the  flux  when  once  established,  as,  for  example,  in  the 
permanent  magnet. 

94.  Just  as  the  presence  of  electric  flux  or  current 
necessitates  the  existence  of  an  E.  M.  F.  to  produce 

it,  so  the  presence  of  a  magnetic  flux  necessitates  the 
presence  of  a  magnetomotive  force  (abbreviated  M.  M.  F.) 
to  produce  it. 

Magnetic  flux,  unlike  electric  flux,  cannot  be  insulated. 
Therefore,  magnetic  flux  cannot  be  confined  to  a  parti- 
cular conductor. 

95.  There  are  two  varieties  of  M.  M.  F.     The  per- 
manent and  the  transient.     A  permanent  mag- 

netomotive force  is  found  in  the  case  of  a  permanent 
magnet.  Here  an  expenditure  of  energy  has  been  initi- 
ally necessary  to  magnetize  the  bar,  but  since  the  bar 
maintains  the  flux  indefinitely  after  the  withdrawal  of 
the  magnetizing  force,  there  must  exist  in  the  magnetized 


bar  a  true  M.  M.  F.  which  sustains  the  flux.  It  is  assumed, 
that  in  the  case  of  the  magnetizable  metals,  the  ultimate 
atoms  or  the  molecules  naturally  possess  true  M.  M.  F.'S, 
which,  however,  distribute  their  magnetic  circuits  in  all 
directions  and  thus  neutralize  each  other's  influences.  On 
the  application  of  the  magnetizing  force,  however,  these 
separate  molecular  M.  M.  F.'S  are  brought  more  nearly 
into  a  common  line  or  direction,  thus  mutually  assisting 
each  other,  and  exerting  a  definite  external  influence. 
When  all  the  molecules  in  a  bar  are  thus  brought  into 
line,  its  M.  M.  F.  is  at  a  maximum  and  the  magnet  is  said 
to  be  magnetically  saturated. 

96.  Most  practical  magnetic  circuits  extend  almost 
throughout  their  entire  length  through  iron.     In 

order  to  force  magnetic  flux  through  a  circuit,  it  is 
necessary  to  wind  the  circuit  with  turns  of  insulated  wire 
and  to  send  a  current  through  these  turns  of  wire.  The 
M.  M.  F.  depends  upon  the  number  of  turns  so  linked  with 
the  circuit,  and  upon  the  strength  of  the  current.  Their 
product,  usually  expressed  in  ampere-turns,  measures  the 
magnetomotive  force  produced. 

97.  The  unit  of  M.  M.  F.  is  the  gilbert,  and  is  such  a 
M.  M.  F.  as  would  be   produced  by —  or  0.7958 

(roughly  0.8)  ampere-turn. 

The  gilbert  and  the  ampere-turn,  as  units  of  M.  M.  F., 
are  related  in  a  similar  manner  to  the  kilowatt  and 
the  horse-power  as  units  of  activity  in  engineering; 
i.  e.y  by  a  numerical  ratio.  It  is  commonly  conveni- 
ent to  express  activities  in  horse-power,  in  order  to 
conform  to  usage,  and  the  classification  of  existing 
machinery ;  but  for  computations  and  simplicity  of  reason- 


93 


ing  and  description,  it  is  usually  advantageous  to  employ 
the  more  fundamental  and  scientific  unit,  the  kilowatt. 
Similarly,  in  dealing  with  M.  M.  F.'S  it  is  commonly  con- 
venient to  express  their  values  in  ampere-turns,  but  for 
purposes  of  computation  and  simplicity  of  reasoning,  it 
is  usually  advantageous  to  employ  the  more  fundamental 
and  scientific  unit,  the  gilbert. 

98.  In  order  to  follow  the  effects  of  iron  on  the  mag- 
netic flux  produced  by  a  current,  as  already  pointed 
out,  let  us  take  the  simple  case  of  an  air-core  solenoid,  or 
hollow  anchor  ring,  of  the  form  shown  in  Fig.  33.  If  such 
a  ring  were  wound  with  100  turns  of  insulated  wire  carrying 
a  current  of  five  amperes,  the  M.  M.  r.  exerted  would  be 
500  ampere-turns  =  628.5  gilberts.  We  may  suppose 
that  in  a  ring  of  the  dimensions  shown,  the  flux  through 
the  core  produced  by  this  M.M.F.  would  be  62.85  webers. 
If  the  ring  were  composed  of  copper  or  wood,  or  any 
material  except  the  magnetic  metals,  this  total  flux  would 
be  practically  the  same.  If,  however,  Fig.  33  represents 
an  iron  solenoid  of  the  same  size  and  wound  with  the 
same  wire,  then  the  magnetic  flux  set  up  in  this  iron  core, 
on  the  passage  of  the  same  magnetizing  current,  would 
be,  perhaps,  500  times  greater.  Here  the  additional  flux 
is  due  to  a  M.  M.  F.,  previously  existing  in  the  iron 
in  a  freely  distributed  state,  but  now  aligned  and  brought 
into  action  by  the  current.  On  the  cessation  of  the  cur- 
rent in  the  solenoid,  this  structural  M.  M.  F.  in  the  iron 
may  remain  largely  intact,  as  shown  in  Fig.  34,  produc- 
ing a  flux  of  say  20,000  webers,  which  is  called  residual 
magnetism.  Although  the  above  are  the  conditions  as 
they  appear  to  actually  exist  in  a  ferric  magnetic  cir- 
cuit, i.e.,  a  magnetic  circuit  of  iron,  still  it  is  practi- 


cally  much  more  convenient  to  assume  that  the  iron  is 
destitute  of  M.  M.  F.,  but  that  it  conducts  magnetic  flux 
much  more  readily  than  air.  That  is  to  say,  it  is  practi- 
cally more  convenient  to  suppose  that  the  iron  does  not 
act  as  a  source  but  as  a  good  conductor  of  flux. 

The  form  of  magnetic  circuit  shown  in  the  above 
figure  is  the  only  form  known  in  which  the  magnetic 
flux-paths  are  definitely  limited,  being  confined,  at  least 

5  Amperes 

M' 


Elte^Engmetr 

FIG.  33. — M.M.F.  OF  500  AMPERE-  FIG.   34.— SAME  COIL  AND  IRON 
TURNS,     OR     628.5     GILBERTS  CORE  WITH  PRIME  M.  M.  F.  RE- 
APPLIED  TO  A  CLOSED  CIRCULAR  MOVED,  LEAVING   A   RESIDUAL 
COIL  WOUND  ON  AN  IRON  CORE,  M.  M.  F.  IN  THE  IRON  OF  ABOUT 
ESTABLISHING   A    M.  M.  F.    OF  200,000  GILBERTS.      RESIDUAL 
250,000  AMPERE-TURNS  OR  312,-  FLUX,  20,000  WEBERS. 
250  GILBERTS.      FLUX,   31,250 
WEBERS. 

for  a  theoretically  wound  solenoid  of  this  type,  entirely 
to  the  interior  of  the  coil.  The  flux-paths  are,  there- 
fore, all  circles,  and  the  density  is  uniform  around  any 
circle. 

99.       When  a  bar  of  iron  is  brought  into  a  magnetic 

flux  and  the  flux  passes  lengthwise  through  it,  the 

bar  thereby  becomes  magnetized.     The  end  where  the 


95 


nlagnetic  flux  enters,  becomes  of  south-seeking  polarity, 
and  the  end  where  it  leaves,  of  north-seeking  polarity, 
ft  is,  for  convenience,  generally  assumed  that  such  a  bar 
concentrates  the  flux  of  the  field  in  which  it  is  placed 
owing  to  the  greater  magnetic  permeability  or  conduct- 
ivity of  the  iron  for  flux.  Although  this  is  a  conveni- 
ent way  of  treating  the  matter  for  practical  purposes, 
yet  it  is  inconsistent  with  the  facts.  A  new  or  local 


FIG.  35. — SECTION  OP  A  COMMON  TYPE  OF  DYNAMO  WITH  MAGNETIC 
CIRCUIT  INDICATED. 


magnetic  circuit  is,  in  reality,  called  into  existence  by  the 
prime  flux,  having  its  local  M.  M.  F.  in  the  iron  bar,  and 
its  flux  similarly  directed  in  the  mass  of  the  bar  and  op- 
positely directed  in  the  air  outside  it,  to  the  prime  flux. 

100.     Fig.  35  represents  diagrammatically  the  distribu- 
tion of  magnetic  flux  in  the  magnetic  circuit  of  a 
particular  type  of  bipolar  dynamo.     Here  the  magnetiz- 
ing coils  M!  M!  and  M2  M2,  when  excited  by  "the  passage  of 


96 


a  continuous  current,  become  the  source  of  a  M.  M.  F. 
which  drives  magnetic  flux  through  the  circuit.  Most  of 
this  flux  passes  through  the  cores,  yoke,  and  pole  pieces 
of  the  magnets,  through  the  air  gaps  A  A  and  the  arma- 
ture core  B.  Some  of  the  flux,  however,  completes  its 
circuit  by  leakage  paths  such  as  a  b  c  and  d  ef,  through 
the  surrounding  air.  The  M.  M.  F.  of  the  coils  M:  M2, 
evidently  depends  upon  the  number  of  turns  of  wire, 
and  upon  the  strength  of  the  circulating  current,  i.e., 
upon  the  number  of  ampere-turns  or  gilberts. 

SYLLABUS. 

A  magnetic  field  is  a  region  traversed  by  magnetic 
flux,  and  is  attended  by  a  stress  in  the  surrounding  ether. 

The  unit  of  magnetic  flux  is  called  the  weber. 

The  unit  of  magnetic  flux-density  is  called  the  gauss, 
or  one  weber  per  normal  square  centimetre. 

The  unit  of  M.  M.  F.  is  the  gilbert,  and  is  the  M.  M.  F. 
produced  by  0.7958  ampere-turn,  approximately. 

Magnetic  flux-density  is  usually  denoted  by  (B,  and  has 
direction  as  well  as  magnitude. 

The  energy  attending  a  magnetic  flux  amounts,  in  non- 

(B2 
magnetic  media,  to  -  -  ergs  per  cubic  centimetre. 

A  closed  circular  coil  or  solenoid,  with  or  without  an 
iron  core,  has  no  external  magnetic  influence ;  -i.e.,  all  its 
magnetic  circuit  is  confined  to  the  interior  of  its  coil. 

Magnetic  flux  is  due  to  the  existence  of  M.  M.  F. 

There  are  two  varieties  of  M.  M.  F.,  the  permanent  and 
the  transient. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 
WEEKLY. 

No.  13.  SEPTEMBEE  8,  1894.       |Xriptiol!! 

Electrical   Engineering  Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED     GRADE. 

Magnetic  Reluctance. 


101.  The  rebuctcvnce  of  a  magnetic  circuit  corres- 
ponds to  resistance  in  the  electric  circuit,  and  is 
that  quantity  which  limits  the  flux  of  magnetism  under  a 
given  M.  M.  F.  The  flux  in  any  magnetic  circuit  can  only 
be  increased  by  either  increasing  the  M.  M.  F.,  or  by  dimin- 
ishing the  reluctance. 

The  unit  of  reluctance  is  named  the  oersted,  after  Hans 
Christian  Oersted,  who,  in  1820,  discovered  the  magnetic 
action  of  an  electric  current.  The  oersted  is  the  reluct- 
ance offered  by  a  centimetre  cube,  of  air-pump  vacuum, 
between  opposed  surfaces. 

The  specific  reluctance  of  a  body  is  called  its  reluctiv- 
ity, and  is  the  reluctance  offered  by  a  centimetre  cube  of 
the  body  between  opposed  parallel  faces,  just  as  the  spe- 
cific electric  resistance  of  a  body  is  called  its  resistivity. 
The  reluctivity  of  nearly  all  substances,  other  than  the 
magnetic  metals,  is  sensibly  that  of  vacuum,  is  equal  to 
unity,  and  is  independent  of  the  flux  density. 

J*       <•»«•      nHnrv-wm  ** 

Published  by 
CTRICAL  E 
203  Broadway,  New  York 

\.G* 

[.Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  June  14,  1894.] 

\rQ9is3i* 


,«.„., 


98 


102.  If  an  anchor  ring  of  copper,  wood,  glass  or  other 
non-magnetic  material  be  uniformly  wrapped  with 
a  magnetizing  coil,  the  reluctance  of  the  circuit  will  de- 
pend upon  the  length  of  the  circuit,  and  on  its  area  of 
cross-section.  In  this  particular  case  all  the  magnetic  flux 
will  be  confined  to  the  interior  of  the  winding,  a  compass 
needle  held  outside  the  winding  indicating  no  deflection. 
Thus,  if  the  mean  diameter  of  the  ring  in  Fig.  36,  be  20 


d, 


Vlec.Enaineer 

FIG.  36, 

A  non-ferric  magnetic  circuit  in  which 
the  magnetizing  force  or  flux  density  is 
uniform  along  any  circle  of  radius,  such 
as  a,  and  equal  to  the  M.  M.  F.  divided  by 
the  circumference,  2  TCCI. 


|r£_  j_  « -MI 

sji    rj 

X v ,— .-^^ 


v 

I 
/ 


*"  .Elec.Enaineer 

PIG.  37. 


A  non-ferric  magnet  circuit  in  which 
the  magnetizing  force  or  flux  density  (in 
the  absence  of  iron)  is  not  the  same  at 
different  parts  of  the  circuit,  and  where 
the  quotient  of  M.  M.  F.  by  the  flux  path 
length  on'y  gives  the  average  intensity. 


cms.,  and  its  cross-section  five  square  centimetres,  the  mean 
length  of  the  magnetic  circuit  will  be  62.83  centimetres, 

and  the  reluctance  of  the  circuit  approximately ^ 
=  12.566  oersteds. 


62.83 


103.     If  now  the  same  coil  be  wound  on  a  core  of  iron 
of  the  same  dimensions,  the  magnetic  flux  within 
the  iron  will  be  far  greater  than  within  the  previous  copper, 
wood  and  glass  core. 


99 


104.  In  the  voltaic   circuit,  as  we  have  seen,  there 
exists  in  nearly  all  cases  that  practically   occur, 

a  distribution  of  electric  potential,  and  the  total  difference 
of  potential  expressed  in  volts  is  the  E.  M.  F.  in  the 
circuit. 

Similarly,  in  the  magnetic  circuit,  in  nearly  all  cases 
that  practically  occur,  there  exists  a  distribution  of  mag- 
netic potential  and  the  total  difference  of  potential  ex- 
pressed in  gilberts  is  the  M.  M.  r.  in  the  circuit. 

The  distribution  of  potential  is  diagrammatically 
indicated  in  any  magnetic  circuit  by  broken  lines, 
which  are  the  sections,  in  the  plane  of  the  paper,  of 
surfaces  connecting  all  points  in  the  magnetic  circuit 
having  the  same  potential,  that  is,  equipotential  sur- 
faces. These  imaginary  equipotential  surfaces  may  be 
made  as  numerous  as  desired.  If  correctly  drawn,  they 
would  everywhere  intersect  the  magnetic  flux-paths  or 
stream-lines  at  right  angles.  In  other  words,  the  flux 
at  a  point  is  always  normal  to  the  equipotential  surface 
through  the  point. 

105.  The  magnetizing  force,  or,  as  it  is  sometimes 
termed,  the  magnetic  force  in  the  circuit,  is  the 

space  rate  of  change  or  gradient  of  the  potential.  That  is 
to  say,  the  magnetizing  force  at  a  point  is  numerically  equal 
to  the  number  of  gilberts  variation  of  potential  per  cen- 
timetre of  flux-path.  Its  direction  is  along  the  lines  of 
flux,  normal  to  the  equipotential  surfaces.  Where  the  rate 
of  change  of  potential  along  the  flux-path  is  one  gilbert 
per  centimetre,  as  guaged  by  an  indefinitely  small  ex- 
cursion, the  magnetic  force  is  unity,  or  one  gauss.  If 
the  rate  of  change  in  potential  per  centimetre  of  flux- 
path  were  500  gilberts,  the  magnetizing  force  there  ex- 


100 


isting  would  be  500  gausses.  It  is  customary  to  express 
magnetizing  force  by  3C,  and  by  the  foregoing  definition, 

3C  =  —  i— ;  where  0,  is  the  magnetic  potential  and  n, 
an 

the  normal  to  the  equipotential  surface  at  the  point.  It 
will  be  seen  that  if,  gilbert  by  gilbert,  all  the  equipoten- 
tial surfaces  in  a  magnetic  circuit  are  drawn ;  where  they 
lie  close  together,  the  number  of  gilberts  per  centimetre 
will  be  great,  and  3C  is  great ;  and  where  they  lie  far  apart, 
the  gradient  of  potential  is  small,  and  5C,  is  small.  "When 
the  equipotential  surfaces  lines  are  straight  and  parallel, 
they  are  also  equidistant,  so  that  3C,  is  uniform,  and  has 
everywhere  the  same  strength  and  direction.  Where 
they  are  concave  or  convex  in  the  direction  of  the  flux, 
there  5C  is  either  convergent  and  increasing,  or  divergent 
and  decreasing. 

"When  the  circuit  is  non-ferric,  the  magnetic  force  3C,  is 
identical  with  the  flux  density,  which  we  have  hitherto 
denoted  by  (B.  When,  however,  the  circuit  contains 
iron,  the  distribution  of  3C,  or  the  prime  flux,  sets  up  a 
structural  M.  M.  F.  in  the  iron,  whose  flux,  merged  with 
5C,  gives  a  resultant  distribution,  represented  by  (&. 

It  is  evident  tha£  since  3C,  is  the  gradient  of  the  poten- 
tial, the  product  of  the  gradient  and  a  small  length  of 
flux-path  gives  the  fall  of  magnetic  potential  in  that 
length.  Summing  up  in  this  way,  along  any  flux-path, 
the  product  of  gradients  and  small  distances,  in  succes- 
sion, the  sums  will  be  the  total  difference  of  magnetic 
potential  in  the  circuit,  or  the  M.  M.  F.  In  other  words, 
the  M.  M.  F.  is  the  line  integral  of  the  magnetic  force. 

Thus,  referring  to  Fig.  30,  if  a,  be  the  radius  in  centi- 
metres of  any  flux-path,  then  the  length  of  that  path 


101 


is  2  TT  #,  and  since  the  intensity  OC,  in  gausses,  has  the 
same  value  all  round  this  circle,  the  line  integral  once 
round  the  circuit  on  this  flux  path  is 

or  or 

2  TT  a  5C  =  £F  gilberts ;  or,  3C  =  _       _  —        gausses  ; 

£1     JT     d  JL/ 

where  .Z,  is  the  length  of  the  flux-path  considered. 

106.  In  general,  however,  this  rule  can  not  be  applied. 
For  if,  in  the  non-ferric  circuit  shown  in  Fig.  37, 
formed  by  a  helix  of,  say,  twenty  turns  carrying  one 
ampere,  if  we  divide  the  M.  M.  F.  of  20  ampere  turns,  i.  e., 
25.14  gilberts,  along  any  path  of  flux,  such  as  a  b  c  d  ef, 
by  the  length  of  the  path,  we  only  obtain  the  average 
magnetic  force.  The  magnetic  force  will  be  greater 
than  this  mean  value  within  the  helix,  and  less  than  this 
mean  value  outside  the  helix  where  the  paths  diverge. 

The  magnetic  force  receives  its  name  from  the  fact 
that  if  a  unit  magnetic  pole  could  be  isolated  (a  physical 
impossibility)  and  introduced  into  the  magnetic  circuit 
at  any  point,  such  as  c,  the  mechanical  force  which  would 
be  exerted  upon  this  unit  magnetic  pole  would  be  equal 
in  dynes  to  the  value  of  3C,  in  gausses,  at  that  point. 

It  has  been  found  that  a  comparatively  simple  relation 
holds  between  the  magnetizing  force  exerted  through 
iron  or  steel,  and  the  apparent  magnetic  reluctance  it 
offers.  We  have  already  pointed  out  that  it  is  not  the 
reluctance,  but  a  structural  M.  M.  r.  which  varies  under 
the  action  of  an  impressed  prime  magnetizing  force. 
Practically,  however,  it  is  convenient  to  regard  the  effect 
as  one  of  change  of  reluctance.  Fig.  38  represents  the 
variation  of  the  apparent  reluctance  of  various  samples 
of  iron  and  steel  under  a  continuously  increased  magnetic 
force.  It  will  be  seen  that  the  reluctance  commences  in 


102 


70  80  90 

Elec.  Engine* 


10  20  30  40  6>" 

MAGNETIZING  FORCE  crC  (GAUSSES)-  PRIME  FLUX, 
FIG.  38. 

Curves  of  reluctivity  in  iron  and  steel  in  relation  to  magnetizing  force. 


103 


all  cases  at  a  certain  value,  and  diminishes  as  the  mag- 
netic force  is  increased,  to  a  critical  value,  where  the 
reluctance  turns  and  commences  rising  steadily  in  a 
straight  line. 

Thus  the  lowest  full  line  curve,  No.  VII,  represents 
the  reluctivity  of  soft  annealed  Norway  iron.  For 
magnetizing  forces  above  3  gausses,  the  reluctivity  fol- 
lows an  ascending  straight  line,  and  at  90  gausses  reaches 
5.45  millioersteds.  If  reluctivity  be  denoted  by  the 
Greek  symbol  v,  we  have,  therefore,  beyond  the  value  of 
3C  =  3 

v  =  (0.3  +  0.057  X)  -T-  1000, 

and  similarly  for  other  samples  of  iron  or  steel. 

Reluctivity  is,  strictly  speaking,  expressed  in  the  c.  G.  s. 
system,  as  a  numeric.  In  Fig.  38,  it  is,  for  convenience, 
expressed  in  millioersteds,  and  the  curves  may  be  there- 
fore directly  interpreted  as  representing  the  reluctance 
of  a  centimetre  cube. 

107.  Since  the  ether  pervades  even  the  densest  mat- 
ter, the  reluctivity  of  any  medium  may  be  re- 
garded'as  the  reluctivity  of  that  ether  and  of  the  medium 
taken  in  parallel.  For  low  values  of  the  magnetizing 
force,  the  reluctivity  of  the  ether  is  so  much  greater  than 
that  of  iron  (say,  1,000  times  greater),  that  it  may  be 
neglected.  This  linear  relation  v  —  a  +  &  3C,  which  ap- 
pears to  hold  from  experimental  evidence,  refers  only  to 
the  metallic  reluctivity  of  the  iron  or  steel,  independ- 
ently of  the  ether  which  prevades  the  metal.  When, 
however,  very  high  magnetizing  forces  are  reached,  the 
reluctivity  of  the  iron  increases  greatly  and  becomes 
much  greater  than  that  of  the  ether,  whose  reluctivity 
therefore  controls.  The  reluctivity  of  iron  and  the 


104 


ether  together  can,  therefore,  never  be  greater  than  unity. 
For  practical  purposes,  however,  iron  is  always  worked 
at  such  magnetizing  forces,  that  its  metallic  reluctivity 
is  always  much  lower  than  unity,  and  consequently  the 
metallic  reluctivity  may  be  taken  within  the  limits  of 
the  diagram  to  be  sensibly  equal  to  the  real  reluctivity 
of  the  ether  and  iron  together. 

SYLLABUS. 

Reluctance  is  that  quantity  in  a  magnetic  circuit  which 
limits  the  flux  under  a  given  M.  M.  F. 

The  reluctivity  of  any  medium  is  its  specific  reluct- 
ance, and,  in  the  c.  G.  s.- system,  is  the  reluctance  offered 
by  a  cubic  centimetre  of  the  body  between  opposed 
faces. 

The  unit  of  reluctance  is  called  the  oersted,  and  is  the 
reluctance  of  a  cubic  centimetre  of  air-pump  vacuum. 

The  reluctivity  of  all  media  with  the  exception  of  the 
non-magnetic  metals  is  practically  the  same,  i.  e.,  unity. 

The  reciprocal  of  magnetic  reluctivity  is  called  mag- 
netic permeability,  and  both  quantities  are  mere  numerics 
in  the  existing  c.  G.  s.  system  of  units,  but  are  probably 
not  simple  numerics  in  the,  as  yet,  undiscovered  true 
relations  of  this  system. 

It  is  erroneous  to  suppose  that  magnetic  permeability 
or  reluctivity  varies  in  iron  under  magnetic  force,  except, 
perhaps,  within  small  limits.  The  apparent  variation  is 
due  to  the  existence  of  a  structural  M.  M.  F.  induced  in 
tlie  iron  under  the  influence  of  a  prime  magnetic  force. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.") 

WEEKLY. 

• 

.No.  U.  SEPTEMBER  15,  1894. 

Electrical   Engineering   Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED     GTCADE 

iVtAQNETIC 


108.     The  fundamental   equation  01  the  magnetic  cir- 
cuit is 

0  =  -  ;  or,  the  webers  =  £ilbert8.  (1) 

(R  oersteds 

From  this  we  6btain 

&  =  <J>  (R,  (2) 

and 

«  =  £         ;  (3) 

There  are,  therefore,  two  ways  of  varying  the  mag- 
netic flux  i:i  any  circuit ;  namely,  by  increasing  the 
M.  M.  F.,  and  by  decreasing  the  reluctamce. 

As  we  have  already  seen,  a  linear  relation  exists  be- 
tween the  reluctivity  of  a  magnetic  metal  and  the  mag- 
netizing force,  but  in  many  practical  magnetic  problems 
it  is  the  flux  density,  rather  than  the  magnetizing  force, 
which  is  known,  and  from  which  the  reluctivity  has  to 
be  determined.  It  becomes  necessary,  therefore,  to  know 

Published  by 
THE    ELECTRICAL   ENGINEER, 

203  Broadway,  New  Vork   N.  Y. 

[Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  June  14,  1894.] 


106 


the  value  of  the  reluctance  of  the  circuit  from  point  to 
point  at  the  existing  flux  density,  in  order  that  the  total 
reluctance  of  the  circuit  may  be  determined. 
From  the  relation 

v  =  a  +  b  3C  (4) 

and  ™ 


corresponding  to  i  =  —  for  the  electric  circuit,  we  obtain 


109.  Fig.  39  represents  a  series  of  curves  showing 
the  reluctivity  of   various  samples  of   iron   and 

steel  at  different  flux  densities  up  to  19  kilogausses, 
taken  from  actual  observations  with  materials  employed 
in  dynamo  construction.  These  curves  conform  to 
equation  (6),  through  the  ascending  branch,  the  corres- 
spoiiding  flux  densities  of  which  are  those  practically 
employed  in  designing  dynamo  machinery.  The  des- 
cending branches  are  not  expressed  by  equation  (6). 
They  belong  to  the  reluctivity  at  early  stages  of  the  mag- 
netizing force  or  flux  density. 

In  order  to  show  the  application  of  the  preceding 
formulae,  we  will  consider  some  cases  similar  to  those 
which  may  arise  in  practice.  We  will  first  take  the  simple 
case  of  the  ferric^  circuit,  in  anchor  ring  form,  shown  in 
Fig.  40,  uniformly  wound  so  as  to  have  no  leakage. 

110.  The  corresponding  case  of  electric  flux  is  shown 
in  Fig.  41,  where  a  number  of  voltaic  cells  are 

connected  in  a  circle  in  series.  Here,  neglecting  the  in- 
fluence of  temperature,  the  resistance  of  the  circuit  be- 
comes independent  of  the  current  density.  The  case  is 


lor 


ABSCISSAE;  FLUX  DENSITY,  GAUSSES(CJ&) 


I      I     I     I     I     I     I     1     I     I     I     I     I     I     I     1     |    | 

I-H'       c$W^*»ooi>ccoiO»-i  j        eo       H*        us        to        t~        oo 

TOTA'   MAGNETIC  INTENSITY  OR  FLUX  DENSITY  (SS)  GAUSSES  EUc.Engineer 

FIG.  39. 

Curves  of  reluctivity  ia  iron  and  steel  in  relation  to  fluy  density,  from  measurements 
by  Kennelly. 


108 


not  an  exact  analogue  unless  the  reluctivity  of  the 
electric  conductor  be  modified  to  suit  the  magnetic 
intensity.  Suppose  this  ring  composed  of  Norway 
iron,  to  be  of  the  dimensions  shown,  and  wound  with 
300  turns  of  insulated  wire  which  carries  a  current  of 
4  amperes.  The  M.  M.  F.  for  this  winding  will  be  1,200 
ampere-turns  =  1508.1  gilberts.  The  magnetizing  force 


Elec-Enaineer 


FIG.  40.  FIG.  41. 

Sections  of  a  Norway  iron  ring.     Ferric  Diagrammatic  representation  of  electric 

magnetic  circuit.  Mean  circumference  circuit.  The  analogue  of  magnetic  cir- 
94.25  cms.  Cross-section  19.635  sq.  cms.  cuit  in  Fig.  40. 

will  be  this  M.  M.  r.  divided  by  the  length  of  the  mag- 
netic circuit,  which  will  vary  between  the  limits  of  the 
outer  and  inner  circumferences.  Taking  the  mean  circum- 
ference, the  mean  prime  intensity  will  be  -1-^°|^4-  =  16.01 
gausses,  and  this  would  be  the  flux  density  if  the  ring 
were  made  of  wood  instead  of  iron.  By  reference  to 
Fig.  38,  it  will  be  seen  that,  at  this  magnetizing  force, 
the  reluctivity  of  Norway  iron  is  0.00121 ;  and,  since 
the  cross-section  of  the  core  is  19.635  sq.  cms.  the  re- 
luctance of  the  circuit  is  -££$£5  X  1.21  =  5.807  milli- 


109 


oersteds  =  0.005807  oersted,  and  the  flux  produced  in 
the  circuit  will,  therefore,  be  T.V|&%*T  =  272,200  webers 
or  272.2  kilowebers,  with  a  mean  flux  density  of  Sfgrfff. 
=  13,860  gausses,  or  webers  per  square  centimetre  of 
cross-section,  i.e.,  13.86  kilogausses. 

111.     Taking  now  the  case  of  an  electro-magnet  of 

the  dimensions  shown  in  Fig.  42,  the  magnetic 

circuit  having  two  air-gaps  in  series,  we  will  first  assume 


01.3  crnj. 


Elec.  Engineer 

FIG.  42. 

Electromagnet  of  wrought  iron,  aero-ferric  circuit.     Air  gaps  %  in.  =  1.27  cm.     Mean 
length  of  magnetic  circuit  140.24  cms.     Cross-section  of  magnetic  circuit  25  sq.  cms. 

that  the  leakage  is  negligibly  small.  The  magnetic  cir- 
cuit is,  therefore,  considered  as  entirely  confined  to  the 
path  of  the  arrows,  1,  2,  3,  4,  leaving  the  other  paths  for 
later  consideration.  Let  us  suppose  that  it  is  required  to 
find  the  M.  M.  r.  which  will  be  necessary  to  produce  a 
flux  of  250  kilowebers,  through  the  keeper.  Assuming 
that  this  magnet  is  entirely  constructed  of  wrought  iron, 
and  that  the  air-gap  is  fixed,  as,  for  example,  by  means 
of  wooden  wedges,  so  that  the  keeper  is  unable  to  ap- 
proach the  poles,  then  the  reluctance  in  each  gap  is 
i-|j  —  0.0508  oersted.  The  density  of  the  flux  in  the 
iron  of  the  circuit  is  10  kilogausses,  and  by  referring  to 


110 


Curve  YL,  Fig.  39,  it  will  be  seen  that  at  this  density  the 
reluctivity  of  ordinary  wrought  iron  is  0.00095.  Since 
the  mean  length  of  the  circuit  in  the  iron  is  137.7 
cms.,  and  its  cross-section  is  25  sq.  cms.,  the  reluctance 
of  the  iron  will,  therefore,  tie  -if -JJ  X  0.95  ==  5.23  milli- 
oersteds  —  0.00523  oersted,  and  the  total  reluctance  of 
the  circuit  0.1068  oersted.  The  M.  M.  F.  required  to  send 


0.001476  Ohm 
309  Volts  Elec.Engineer 


FIG.  43. — ELECTRIC  CIRCUIT  ANALOGUE.     WITHOUT  LEAKAGE. 
250,000  webers  through  this  circuit,  will  be  250,000  X 
0.1068  =   26,700   gilberts  =  21,256  ampere-turns.     If 
the  spools  have  the  same  winding  there  must  be  10,628 
ampere-turns  on  each  spool. 

The  corresponding  electric  case  is  shown  in  Fig.  43. 

112.  Let  us  now  assume  that  the  electro-magnet  pos- 
sesses an  appreciable  leakage,  and  let  us  assume 
that  this  leakage  takes  place,  as  shown  diagrammatically 
in  Fig.  42,  along  the  paths  5,  6,  7, 8,  —9, 10, 11, 12—  and 
13,  14,  15,  16.  Let  it  be  ascertained  that  this  leakage 
amounts  to  33|  per  cent,  of  the  total  flux,  so  that  for 


Ill 


every  100  webers  of  flux  in  the  interior  of  the  field  cores 
only  66 1  pass  through  the  keeper.  It  is  required  to  find 
the  M.  M.  F.,  which  will  enable  250  Mlowebers,  as  before, 
to  pass  through  the  keeper  under  these  circumstances. 

The  effect  of  leakage  is  not  only  to  reduce  the  effective 
cross-section,  which  may  carry  the  main  circuit  flux,  but 
also,  owing  to  the  increase  in  density,  to  increase  the  re- 
luctivity of  that  reduced  cross-section. 

Similarly,  if  it  be  known  that  the  leakage  flux  through 
the  yoke,  in  the  path  6,  7,  is  50  kilo  webers,  the  total 


KEEPER 

FIG.  44. — ELECTRIC  CIRCUIT  ANALOGUE.     WITH  LEAKAGE. 

flux  through  the  yoke  will  bo  300  kilowebers,  and  the 
flux  density  there  -%°-  =  12  kilogausses.  At  this  den- 
sity, the  reluctivity  of  wrought  iron  by  Curve  VI.,  Fig. 
30,  is  seen  to  be  .001316. 

113.  Referring  to  Fig.  44,  which  represents  the  elec- 
trical analogue  of  this  case,  observe  that  each  core 
may  be  regarded  as  the  seat  of  an  E.  M.  r.  impressed  on 
three  independent  circuits,  numbered  to  correspond  with 
Fig.  42.  J£A,  7?B,  and  7?c,  are  fixed  reluctances  through 
air,  depending  upon  the  dimensions  and  arrangement  of 


112 


the  various  parts  of  the  magnet.  They  have  perfectly 
definite  values,  but  these  values  may  be  very  tedious 
and  difficult  to  compute.  The  reluctances  Oi9  <72,  63, 
£4?  <??  ft?  ^3  and  ^e  depend  upon  the  share  of  iron 
allotted  to  each  branch  circuit,  and  also  to  the  flux  den- 
sity. We  proceed  to  determine  the  various  reluctances 
6y2,  '^3,  G,  ^?5,  ^j?  an(l  #a>  in  tne  main  circuit,  and  call- 
ing their  sum  (R,  we  have  the  simple  relation 


G 

o 

UP 

i 

£ 

gj 

F 

1 

18*° 

- 

M 

* 

s 

Wc 

v.-,    C?Cr 

3     . 

• 

*j  en 

Reluctance  Oersteds. 

E  2 

.r  w 

d 

o 

A 

0 

o  fc  * 

LjS 

$i 

0    ^ 

I 

«  cr 

^uiz 

Is 

sa 

J2  w 

(2 

J 

H 

C/3 

H 

Q 

OS 

Core  

3° 

25 

16.667 

375 

15 

3-°77 

,-^X  ^=0.005539 

Yoke.... 

38.85 

25 

20.833 

300 

12 

1.316 

38.85  X1-3i6 

20.833       looo"0-00245^ 

Core  .... 

3° 

25 

16.667 

375 

15 

3-°77 

I^7X^=o.ooS539 

Air-gap.. 

1.27 

25 

25 

250 

10 

1000 

1.27 
—  X  i        =0.050800 

Keeper  .. 

38.85 

25 

25 

250 

IO 

0-95 

38  85     0.95 

Air-gap. 

1.27 

25 

25 

250 

10 

1000 

1.27   ^  T       0.050800 

25                     o.i  1  6608 

To  force  250  t:ilowebers  through  the  main  circuit 
through  this  reluctance,  a  M.  M.  r.  will  be  needed  of 
250,000  X  0.116608  =  29,152  gilberts,  or  23,200  am- 
pere-turns— 11,600  to  each  spool. 

SYLLABUS. 
The  fundamental  equation  of  the  magnetic  circuit  is 

£F  gilberts 

=  S°rtheWeberS^  oersteds' 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 
WEEKLY. 

No.  15.  SEPTEMBER  22,  1894. 

Electrical   Engineering  Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED     GRADE. 

ELBCTROMAQNBTS. 


114.  The  polarity  of  an  electromagnet  may  be  deter- 
mined by  noticing  the  character  of  the  magnetiz- 
ing coils,  whether  right-handed  or  left-handed,  and  the 
direction  in  which  the  current  traverses  them.    A  right- 
handed  helix  carries  the  flux  in  the  same  direction  as 
that  in  which  the  current  advances  along  the  helix,  while 
a  left-handed  helix  carries  the  flux  in  the  opposite  direc- 
tion of  the  advance  of  the  current..     As  already  pointed 
out,   the  flux   in  an  electromagnet  is   of  two  distinct 
characters ;   namely,  the  prime  or  magnetizing  flux,  and 
the  induced  or  structural  magnetic  flux,  which  is  called 
into  play  by  the  action  of  the  prime  flux. 

115.  Electro-magnets  may  be  divided  into  two  classes; 
namely,  the  tractive  and  the  portative ;  the  former 

are  designed  to  exert  a  pull  on  their  armature  at  some 
distance  from  the  poles,  and  the  latter  are  designed  to 
support  a  pull  upon  the  armature  when  the  armature  is 
placed  in  contact  with  the  poles. 

Published  by 
THE   ELECTRICAL  ENGINEER, 

203  Broadway,  New  York   N.  Y. 

[Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  June  14,  1894.] 


114 


In  all  practical  cases  an  electromagnet  exerts  a 
pull  upon  the  iron  or  steel  of  the  armature  whether 
the  armature  be  separated  from  the  poles  by  an  air- 
gap,  or  whether  it  be  in  actual  contact  with  the  poles, 
and  the  same  process  of  calculation  has  to  be  employed 
in  each  case  in  order  to  compute  the  attractive  force. 
This  process  is  substantially  as  follows :  The  reluctances 
of  the  different  parts  of  the  circuit  have  to  be  de- 
termined and  summed,  the  M.  M.  F.  acting  in  the  cir- 
cuit has  then  to  be  ascertained,  and  from  these  the  flux 
in  the  circuit  is  deduced.  From  the  flux  and  its  distri- 
bution, the  flux  density  in  the  air-gap  between  the  keeper 
and  poles  has  to  be  found,  and  from  this  flux  density, 
the  intensity  of  the  attractive  force  is  determined  from 
point  to  point.  The  total  attractive  force  on  the  arma- 
ture will  be  the  surface  integral  of  this  attractive  force 
over  the  area  of  the  attracting  surfaces. 

116.  The  fundamental  law  of  attractive  force  is  as 
follows:  At  any  element  of  surface  on  iron  or 
steel  at  which  flux  enters  or  emerges  perpendicularly, 
the  attractive  force  in  dynes,  exerted  upon  the  element, 
will  be  the  product  of  the  elementary  surface  area  into 
the  square  of  the  flux  density  (expressed  in  gausses), 
divided  by  8  TT  ;  that  is, 

dF=dS—  dynes, 

STT    J 

where  (B,  is  the  normal  flux  density ;  d  F,  the  element 
of  attractive  force,  and  d  $,  the  element  of  surface  in 
square  centimetres ;  and  this  force  will  be  exerted  along 
the  flux  paths,  or  perpendicular  to  the  surface.  If,  how- 
ever, the  entering  or  emerging  flux  makes  an  angle  6, 
with  the  normal  to  the  surface,  then  the  above  rule  re- 


115 


quires  slight  modification.  The  equivalent  normal 
surface,  on  which  the  attractive  effort  is  exerted,  is  d  S 
cos  0,  so  that  the  attractive  force  becomes, 

1     C1 a    /T»  9 

dynes, 


Sx 

exerted  in  the  direction  of  the  flux-paths  of  which  the 
component  perpendicular  to  the  surface  is, 


FIG.  45. 

Flux  normal  to  opposed  plane  parallel 
polar  surfaces. 


Elec.  Engineer 


FIG.  46. 

Flux  oblique  to  polar  surfaces. 


117.  Let  A  B  c  D,  and  A'  B'  c'  D',  Fig.  45,  be  portions 
of  two  parallel  plane  polar  faces  of  iron  between 
which  the  magnetic  flux  passes  perpendicularly  across 
the  intervening  space  A  A',  or  c  c'.  If  the  flux  intensity 
is  uniform  over  these  surfaces  and  equal  to  five  kilo- 
gausses,  then  the  mechanical  force  exerted  between  any 
pair  of  opposed  unit  areas,  such  as  the  shaded  portions 
e  f  ff  h,  and  e'  f  g'  hr,  each  one  square  centimetre,  will 


116 


be  500Q  X  50QQ   or   approximately   994,800   dynes,    or 

8  7T 

1,015  grammes  weight  (2.238  pounds),  at  Washington. 
Since  the  total  area  A  B  c  D,  or  A'  B'  c'  D'  is  25. square 
cms.,  the  total  mechanical  force  exerted  between  these 
surfaces  will  be  25.375  kilogrammes  (55.95  pounds).  The 
magnitude  of  the  attractive  force  does  not  depend  upon 
the  distance  A  A',  separating  the  polar  faces,  nor  does  it 
depend  upon  the  direction  of  the  flux  between  them. 
All  that  is  essential  is  that  the  flux  should  be  perpendi- 
cular to  the  faces.  Increasing  the  air-gap  will,  in  prac- 
tice, usually  diminish  the  total  flux,  and,  therefore,  the 
flux  intensity  over  the  surfaces,  also  causing  the  flux 
paths  to  deviate  from  the  perpendicular  by  lateral  dif- 
fusion ;  but  if  these  secondary  effects  could  be  compen- 
sated and  removed,  the  attraction  between  the  surfaces 
would  not  vary  witli  the  length,  of  air-gap. 

118.  Fig.  46  represents  a  case  where  the  flux  passes 
between  the  parallel  polar  faces  at  an  angle  /?, 
with  their  normal.  If  a  I  c  d,  and  e  f  g  A,  are  areas 
limited  by  the  flux-paths  a  e  p,  1}  I  q,  c  g  r  and  d  h  n, 
then  the  attractive  force  between  these  areas  will  be 
such  as  would  be  experienced  by  two  surfaces  each  of 
the  area  Icl  g  m,  standing  perpendicularly  across  the 
flux.  If  a  b  G  d,  and  e  f  g  A,  have  each  an  area  of  one 
square  cm.,  the  surface  k  I  g  m,  will  have  an  area  of 
cos  /?  square  cms.  With  10  kilowebers  passing  through 
each  of  the  shaded  areas,  the  flux  density  will  be 

®  = ^ .     The  attractive  force  between  two  opposed 

cos/3 

/r>2 

parallel  surfaces  of  area  Tc  I  g  m,  will  be  —  cos  /?  ex- 

8  71 


117 


erted  along  the  flux  paths.     The  component  of  this  ten- 
sion exerted  across  the  actual  surfaces  abed,  and  ef  g  k, 

(B2 

will  be  —  cos  2/9,  and  the  component  tending  to  make 
8  JT 


II 

ie.000 

15.000 
14,000 
13,000 
18,000 
11,000 
10,000 
9,0000 
8,0000 
7,0000 
0,0000 
6,0000 
4,0000 
3,0000 
2.0000 
1,0000 

!! 

I 

16,000,000 
15,000,000 
14,000,000 
18,000,000 
12,000,000 
11,000,000 
10.000,000 

9.000,000 
8,000,000 
7.000,000 
6,000,000 
6,000,000 
4,000,000 
8,000,000 
2.POO.OOO 

l.ooo.ooo 

• 

Ii 

1 

200 
190 

uo 
III 

170 

160 
150 
140 
130 

IM 

no 

100 
90 

70 
CO 

40 
30 

, 

/ 

I 

II] 

/ 

ii 

A 

/ 

A 

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t 

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'/ 

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f 

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£ 

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r-^ 

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-^ 

Mis 

KILOGAUSSES 

B2  9  &  2  9  tf  1  3  1  1  £  £  2  2  2  I  2  2  2  d 

«K  *  *.  a 
p-  ^  a 


KILOWEBERSPERSQ. 


Elec.Engineer 
Cvt\e&  representing  the  intensity  of  magnetic  stress,  for  all  values  of  30 

from  O  to  20  Kilogausses.      O  to  129  Kilowebers  per  sq.  in. 
I  in.  dynes  per  square  centimetre.il  in  grammes  weight  per  square  centimetre 
III  jn  pounds  weight  per  square  inch. 

FIG.  47. 
these    surfaces    shear    across    one    another   would    be 

(B21 

-  sin  ft  cos  ft. 

O  71 

In  practice,  the  useful  flux  exerting  tractive  force  be- 


118 


tween  the  polar  surfaces  of  electromagnets  may  be  con- 
sidered as  crossing  those  surfaces  at  right  angles,  so  that 
the  simpler  formula  may  generally  be  applied. 

119.  As  a  consequence  of  the  preceding  formulae  it 
is  evident  that  the  active  polar  surfaces  of  a  port- 
ative electromagnet  should  have  as  great  an  area  as  pos- 
sible, provided  that  the  flux  density  over  them  be  made 
as  great  as  possible.  In  other  words,  the  polar  surfaces 
should  have  maximum  areas  consistent  with  their  mag- 


Elec.Engineer 

FIG.  48. 
Section  of  Portative  Electromagnet  through  Axis,  and  Polar  Surfaces. 

netic  saturation.  The  curves  in  Fig.  47  show  that  at  a 
density  of  18  kilogausses,  which  is  readily  obtainable  in 
ferric  magnetic  circuits  employing  soft  Norway  iron,  the 
attraction  becomes  1 3.14  kilogrammes  per  square  cm.,  or 
186.6  pounds  per  square  inch  of  opposed  polar  surfaces. 

120.     A  convenient  practical  form  of  electromagnet 

for  sustaining  heavy  weights  is  shown  in  Fig.  48. 

The  magnetic  circuit  is  indicated  by  the  lines  of  arrows. 


119 


The  external  surface  of  the  magnet  when  the  keeper 
is  in  place,  being  entirely  of  iron,  the  magnet  is  usually 
described  as  belonging  to  the  ironclad  type.  The  con- 
tact polar  surfaces  should  be  carefully  planed  and  kept 
clean  if  the  best  attractive  results  are  to  be  obtained. 
The  space  allowed  for  the  exciting  coil  is  made  as  small 
as  is  consistent  with  saturation  of  the  polar  surfaces. 
The  limiting  M.  M.  F.  that  can  be  employed  for  a  given 
winding  space  depends  upon  the  heating  of  the  coil  by 
the  current,  and  not  upon  the  size  of  the  wire.  Practi- 
cally, however,  a  large  wire  with  few  turns  can  be  better 
protected  against  damage  from  a  high  temperature,  than 
a  small  wire  with  many  turns.  It  is  essential  that  the 
flux  density  should  be  a  maximum  in  the  circuit  at  the 
polar  surfaces,  and  for  this  reason  the  surface  area  of 
the  inner  core  and  outer  ring  should  be  kept  equal  while 
a  slight  constriction  in  the  iron  should  'be  made  at  the 
poles. 

If  such  a  magnet  have  a  cross-sectional  area  of  20 
square  cms.  at  the  inner  or  core  polar  surfaces,  and  also 
10  square  cms.  at  the  outer  or  annular  polar  surfaces,  the 
portative  power  of  the  magnet  may  readily  be  40  X  15 
=  600  kilogrammes  weight. 

121.  When  an  electromagnet  has  to  exert  a  tractive 
force  upon  its  armature  at  a  distance,  through  one 
or  more  air-gaps  of  given  length,  the  best  area  of  polar 
surface  to  employ  with  a  fixed  M.  M.  F.,  and  the  size  of 
magnet  are  those  which  make  the  reluctance  of  the  air, 
equal  to  the  reluctance  of  the  iron  in  the  circuit.  If, 
for  example,  an  electromagnet  has  two  poles  each  four 
centimetres  in  diameter,  and  the  air-gap  or  distance  be- 
tween poles  and  armature  be  0.25  cm.,  then  the  area  of 


120 


each  pole  face  will  be  12.57  square  cms.,  and  the  reluct- 
ance of  the  air  0.0398  oersted.  If  the  reluctance  in  the 
iron  be,  say,  0.050  oersted,  under  these  conditions  with 
the  M.  M.  F.  employed,  it  will  be  advantageous  to  increase 
the  air  reluctance  by  constricting  the  polar  surfaces  until 
the  air  and  iron  reluctances  equate.  This  assumes,  how- 
ever, as  negligible,  leakage  and  diffusion  of  flux  at  the 
polar  surfaces.  In  consequence  of  leakage  and  diffusion, 
it  is  preferable  to  make  the  air  reluctance  somewhat  less 
than  the  iron  reluctance. 

SYLLABUS. 

The  direction  of  magnetic  flux  within  a  coil  is  in  the 
direction  along  which  the  current  traverses  the  coil  if 
the  coil  be  right-handed,  and  opposite  to  the  direction 
of  the  current  if  the  helix  be  left-handed. 

The  fundamental  law  of  tractive  force  upon  a  mag- 
netized surface,  at  which  flux  enters  or  issues  perpendir 

cularly,  is  d  F  =  d  8—  dynes. 

8  7T 

Portative  electromagnets  are  designed  to  have  as  large 
an  area  of  saturated  polar  surfaces  as  possible. 

Powerful  tractive  magnets  are  designed  to  have  their 
reluctance  about  equally  divided  between  air  and  iron. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 
WEEKLY. 

No.  16.  SEPTEMBER  29,  1894. 

Electrical   Engineering  Leaflets, 


—BY— 

Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A,  S. 


ADVANCED     GRADE. 

INDUCED    EX  IVL  K. 


122.  Whenever  relative  motion  exists  between  mag- 
netic flux  and  an  electric  conductor,  so  that  one 

moves  across  the  other,  an  E.  M.  F.  will  be  set  up  in  the 
conductor.  This  relative  motion  between  flux  and  con- 
ductor may  occur  in  two  ways  ;  namely, 

(1.)  When  the  conductor  moves  across  the  flux. 

(&)  When  the  flux  moves  across  the  conductor. 
Both  cases  may  occur  together,  but  in  (1)  we  suppose 
that  the  flux   may  be  considered  as  at  rest,  and  in  (2), 
that  the  conductor  may  be  considered  at  rest. 

123.  We  will  now  consider  case  (1),  in  which  the 
conductor  moves  across  a  magnetic    flux.      Al- 
though the  mechanism  by  which  E.  M.  F.  is  induced  is 
unknown,  yet  the  E.  M.  F.  produced  is  directly  propor- 
tional to  the  total  amount  of  flux  per  second  cut  by  the 
conductor,  and  this  clearly  depends  on  two  quantities ; 
namely,  upon  the  velocity  of  the  conductor  across  the 
flux,  and,  upon  the  intensity  of  the  flux. 

Published  by 
THE   ELECTRICAL  ENGINEER, 

203  Broadway,  New  Vork   N.  Y. 

[Entered  as  second-class  matter  at  the  New  York,  N.  YM  Post  Office,  June  14,  1894.] 


122 


124.  Consider,  first,  a  uniform  magnetic  flux,  whose 
intensity  at  a  given  point  is  equal  to  (B,  and  is  di- 
rected as  shown  by  the  arrows,  Fig.  49.  A  rectilinear 
conductor  A  B,  normal  to  the  flux,  is  moved  in  a  direction 
normal  to  the  flux  with  a  velocity  v,  which  would  carry 
it  in  one  second  to  A'  B'.  Then  the  total  amount  of  flux 
cut  per  second  would  be  the  amount  passing  through  the 
rectangle  ABB'  A', -and  this  is  clearly  equal  to 

e  =  v  I  (B  c.  G.  s.  units  of  E.  M.  F. 

Suppose,  however,  that  a  conductor  lying  in  a  position 
oblique  to  the  flux,  as  shown  in  Fig.  50,  is  moved  in  a 


B     ^ 

*  ^ 

-* 

*>'    ^ 

N< 
>* 

/l^*-   B' 

-* 

^^^^^x 

b' 

"*•  ^ 

A^*^C^  **•  ^i 

''T~-^ 

••». 

^  i  ^  ^  ^  i  H 

ar'--^j^^^^B' 

3   "». 

U         ^          T^      1 

~k 

^       ^       -*b|    *i 

>          S^ 

'A           ^        **+% 

•^    ,--.    ^/     i/,                  ,x 

V.                ~Sk.          -X^            1^1 

:\^^B 

R>^A  / 

^   <^'*/^.      ^^' 

^ 

^ 

FIG.  49  FIG.  50.  FIG.  51. 

Conductor  normal  toflux.  Conductor  oblique,  to  flux,  Conductor  oblique  to  flux, 
moving  in  direction  normal  moving  of  conductor  in  di-  moving  in  direction  othque 
to  flux.  rection  normal  to  flux.  to  flux. 

direction  normal  to  the  uniform  flux  with  a  uniform 
velocity  v ;  then  the  total  amount  of  flux  cut  per  second 
will  be  that  enclosed  by  the  rectangle  A  J  1}'  A',  where 
A  J,  is  the  virtual  length  of  the  conductor  equal  to 
A  B  cos  /9,  that  is,  the  projected  length  normal  to  the  flux, 
and  the  E.  M.  r.  is  equal  to 

e  =  v  I  cos  /9  (B          c.  G.  s.  units. 
If  both  the  position  of  the  conductor,  and  its  motion 
are  oblique  to  the  direction  of  the  flux,  as  in  Fig.  51, 


123 


then  the  total  flux  cut  per  second  will  be  that  enclosed 
by  the  rectangle  A  b  ~b'  A',  where  A  B,  is  the  virtual 
length  of  the  conductor,  as  before,  and  A  a',  is  the  virtual 
velocity  normal  to  the  flux,  or  A  A'  cos  «.  So  that 

e  =  v  cos  a  I  cos  ft  &  c.  o.  s.  units. 

Since  one  volt  equals  108  c.  G.  s.  units  of  E.  M.  F.,  the 
E.  M.  F.  as  above  obtained,  must  be  divided  by  10*  in 
order  to  obtain  its  value  in  volts. 


FIG.  52. 

125.     The  direction  of  the  induced  E.  M.  F.  varies  both 
with  the  direction  of  the  flux  and  with  the  direc- 
tion of  the  motion.     The  simplest  rule  for  memorizing 
this  direction  is,  probably,  Fleming* B  hand  rule. 

If  the  right  hand  be  held,  as  shown  in  Fig.  52,  with 
the  extended  /ore-finger  pointing  in  the  direction  of  the 
/"lux,  and  the  thumb  in  the  direction  of  the  motion,  then 


124 


the  E.  M.  F.  induced  will  be  directed  along  the  direction 
in  which  the  middle  finger  points. 

126.  In  practice  when  a  conductor  is  moved  through 
a  magnetic  flux,  it  generally  happens  that  neither 

the  intensity  of  the  flux  nor  the  velocity  in  the  direction 
of  motion  is  uniform.  Nevertheless,  the  above  law  is 
true  for  any  small  element  of  the  conductor  at  any  mo- 
ment, when  its  direction  and  the  intensity  of  the  flux  in 
which  it  moves  are  taken  into  account. 

127.  Turning  now  to  case  (2)  where  the  flux  moves 
across  a  conductor.     The  fundamental   rule  re- 
mains the  same   as  in  the  preceding  case ;  if  v,  be  the 
velocity  of  the  field  at  any  point,  where  the  intensity  is 
<&,  and  I  be  the   virtual   length   of  conductor  at  right 
angles  to  the  flux  and  the  motion,  then  the  E.  M.  F.  in 
c.  G.  s.  units  is  v  (B  Z,  as  before. 

128.  In  order  that  the  induced  E.  M.  F.  in  a  conductor 
may  produce  a  current,  the  circuit  of  that  con- 
ductor must  be  closed,  that  is,  a  conducting  loop  must 
be  formed,  although  only  a  portion  of  this  loop  may  be 
active  in  cutting  through  flux  and  generating  E.  M.  F. 
It  is  obviously  the  same  whether  we  speak  of  the  rate  at 
which  the  portions  of  the  loop  are  cutting  through  flux, 
or  of  the  rate  at  which  a  loop  is  enclosing  flux,  since  the 
sum  of  all  the  lines  cut  through  per  second  around  a 
loop  must  be  equal  to  the  amount  of  flux  enclosed  by 
the  loop  in  that  time.     Similarly,  when  flux  is  withdrawn 
from  a  loop,  the  E.  M.  F.  will  be  introduced  around  the 
loop  in  the  opposite  direction.     All  these  results  may  be 
included  in  the  following  equation  : 

«=<** 

dt' 


125 


where  0,  is  the  flux  enclosed  by  the  loop  (webers)  in  the 
positive  direction,  and  — — -     the  instantaneous   rate   of 

Ci   t 

change  of  that  flux. 

129.     A  consideration   of   Figs.  49,  50  and   51   will 

render  it  -evident  that  E.  M.  F.  is  never  produced 

by  the  relative  motion  of  magnetic  flux  and  a  conductor, 

unless  a  change  exists  in  the  amount  of  flux  enclosed  by 


FIG.  53. 

Conducting  ring  normal  to  flux,  mov- 
ing in  plane  normal  to  uniform  flux. 


FIG.  54. 

Conducting  ring  normal  to  flux,  mov- 
ing in  a  plane  normal  to  a  non-uniform 
flux. 


the  conducting  circuit.  It  is  evident,  therefore,  that  if 
the  conducting  ring,  shown  in  Fig.  53,  though  normal  to 
the  uniform  magnetic  flux,  and  moving  at  right  angles 
to  such  flux,  so  as  to  cut  the  flux,  has,  nevertheless,  no 
resultant  E.  M.  F.  generated  in  it,  since  at  any  moment  of 
time  the  flux  it  encloses  is  constant ;  or,  if  regarded  from 
the  standpoint  of  Fig.  49,  the  E.  M.  F.  generated  by  the 
cutting  in  the  upper  half  of  the  loop,  is  exactly  equal 
and  opposite  to  the  cutting  in  the  lower  half. 


126 


The  conducting  ring,  shown  in  Fig.  54,  placed  normal 
to  the  non-uniform  flux,  if  moved  in  its  own  plane  in 
any  direction  except  in  the  directions  F  G,  or  G  F,  will 
have  a  resultant  E.  M.  F.  generated  in  it,  since  the  amount 
of  flux  enclosed  by  the  loop  will  otherwise  increase  or 
diminish. 

130.     If  a  conducting  loop,  placed  in  a  uniform  mag- 
netic flux,  be  rotated  about  any  axis,  as,  for  ex- 
ample, about  the  axis  H  K,  in  Fig.  55,  a  resultant  E.  M.  F. 


FIG.  55. 

Rotation  of  a  Loop  in  a  Magnetic  Flux. 

will  be  induced  in  it,  since  the  amount  of  flux  enclosed 
by  the  loop  will  vary.  Thus,  in  rotating  the  loop  from 
A  to  A',  the  flux  enclosed  will  be  reduced  from  the  total 
area  ABC,  to  the  virtual  area  def.  Since  the  value 
of  the  E.  M.  F.,  at  any  instant,  is  the  time  rate  of  change 
of  the  flux  enclosed  by  the  circuit,  it  is  evident  that  the 
maximum  E.  M.  F.  is  produced  when  the  plane  of  the  loop 
is  parallel  to  the  direction  of  the  flux. 


12Y 


131.  When  a  current  through  a  conductor  is  chang- 
ing its  strength,  there  will,  as  we  have  already 
seen,  be  a  change  in  the  amount  and  intensity  of  the 
flux  surrounding  the  conductor.  Since  the  entire  con- 
ducting circuit,  in  which  the  current  flows,  may  be 
regarded  as  a  loop,  or  combination  of  loops,  these  varia- 
tions in  the  flux  linked  with  the  conducting  loop  will 
induce  in  the  conductor  an  E.  M.  F.  of  exactly  the  same 
strength  as  though  the  current  remained  unchanged,  but 
the  same  flux  variations  passed  through  the  conducting 
loop.  This  E.  M.  F.  induced  in  a  circuit  by  variations  in 
its  current  strength  is  known  as  a  self-induced  E.  M.  F., 
or  an  E.  M.  F.  of  self-induction. 


Projection  of  Magnetic  Flux  through  Conducting  Loops. 

132.  If  a  current  be  sent  through  the  electromagnetic 
helix,  shown  in  Fig.  56,  in  such  a  direction  as  to 
produce  the  poles  s,  N,  then  the  flux  established  is  shown 
in  part  by  the  curved  arrows,  in  the  neighborhood  of  the 
north  pole.  As  this  flux  emerges,  it  will  pass  through 
the  loops  A,  D,  B,  and  c;  but  whereas  the  same  amount  of 
flux  passes  through  each  of  the  two  loops  A,  or  B,  is 
greater  than  that  which  flows  through  p,  the  E.  M.  F.  gene- 
rated in  A,  or  B,  during  the  change  will  be  greater  than 
that  in  c,  while  the  double  loop  D,  will  have  double  the 
E.  M.  F.  in  it.  The  direction  of  the  E.  M.  F.  in  these  loops, 


UNIVERSITY 


128 


on  making  the  magnet  circuit,  is  opposite  to  that  on 
breaking :  for  in  one  case  the  flux  passes  through  the  loop 
to  the  right,  and  in  the  other  case;  to  the  left.  Even 
when  the  existence  of  the  flux  that  passes  through  the 
loop  cannot  be  determined  by  the  aid  of  a  compass 
needle,  as,  for  example,  in  Fig.  57,  where  the  closed  cir- 
cular coil  is  linked  with  three  separate  conducting  loops 
j  k  Z,  h  e  f  g,  and  m,  yet  on  varying  the  current  in 
the  coil  the  same  E.  M.  F.  will  be  induced  in  all  three 


FIG.  57. 

Closed  Circular  Coil  linked  with  three  Loops  of  Conductor. 

loops.  This  case  is  apparently  an  independent  demon- 
stration of  the  fact  that  the  velocity  of  the  propagation 
of  magnetic  disturbances  is  finite. 

SYLLABUS. 

If  $,  be  the  total  flux  in  webers  linked  with  a  con- 
ducting circuit  in  the  positive  direction,  then  ^-^  X  10"8 

cL  t 

is  the  E.  M.  F.  induced  in  that  circuit  in  International 
volts. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER,] 


WEEKLY. 


1  7  fWrmvT?  ft    1  SQ4.         Price,     -    10  Cents. 

rOBER  6,  1    J4.        Subscription,  $3.00. 

Electrical   Engineering   Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED     GRADE. 

DYNAMO. 


133.     A  continuous  current  dynamo,  depending  as  it 
does   for   the   production   of  its   E.  M.  F.  on  the 
movement  of  conductors  through  a  magnetic  flux,  de- 
termines the  magnitude  of  that  E.  M.  F.  in  accordance 
with  the  relation, 

E  =  $  n  w  c.  G.  s.  units, 

—  0  n  w  10~8  volts. 

where  <#,  is  the  total  useful  magnetic  flux  through  one 
pole  passing  into  the  armature  (webers) ;  n,  the  number 
of  revolutions  made  by  the  armature  per  second;  and  w, 
the  number  of  conductors  on  the  surface  of  the  arma- 
ture counted  in  one  complete  revolution.  That  is  to 
say,  the  E.  M.  F.  is  directly  proportional  to  the  product 
of  the  total  useful  magnetic  flux  through  each  pole,  the 
rate  of  speed  of  the  armature,  and  to  the  number  of 
turns  of  wire.  Thus,  Fig.  58,  represents  a  four-pole 
generator  for  550  volts.  The  useful  flux  through  each 

Published  by 

THE   ELECTRICAL  ENGINEER, 
203  Broadway,  New  York   N.  Y. 

Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  June  14,  1894.] 


130 


pole  may  be,  say,  55  megawebers ;  there  are,  say,  200 
conductors  embedded  in  the  surface  of  the  armature, 
and  the  speed  of  rotation  is  assumed  to  be  300  revolu- 
tions per  minute,  or  tive  revolutions  per  second.  The 
E.  M.  F.  generated  by  the  machine  is,  therefore, 

L  =  5  X  200  X  55  X  106  X  10~8  =  550  volts. 


FIG.  58. 

550  Volt  Four-Pole  Generator. 

134.  The  output  of  a  generator,  or  its  capacity,  is 
usually  expressed  in  kilowatts,  and  is  the  electri- 
cal activity  which  the  machine  can  maintain  at  its  ter- 
minals. This,  within  wide  limits,  is  independent  of  the 
electromotive  force ;  that  is  to  say,  the  100  K.  w.  machine 
can  be  constructed  for  1,000  volts  and  100  amperes,  or 
for  100  volts  and  1000  amperes,  or  50  volts  and  2,000  am- 
peres output.  There  is,  however,  a  practical  limit  to  the 
E.  M.  F.  which  can  be  obtained  from  a  machine  without 


131 


altering  its  rating ;  for,  very  small  E.  M.  r.'s  may  require 
such  massive  construction  in  their  commutators  and  ad- 
jacent conducting  parts,  to  carry  off  the  enormous  cor- 
responding currents  generated,  that  the  whole  structure 
of  the  machine  may  require  to  be  modified,  while,  when 
high  electromotive  forces  are  reached  the  great  thickness 
of  insulating  material  required,  may  so  reduce  the  avail- 
able winding  space  as  to  seriously  reduce  the  output. 

135.  When  a  dynamo-electric  generator  is  operated 
on  open  circuit,  it  is,  of  course,  doing  no  work, 

since  the  resistance  of  its  external  circuit  is  infinite.  As 
the  resistance  of  the  external  circuit  is  decreased,  the 
amount  of  work  in  its  circuit  increases,  until,  when  the 
external  circuit  has  no  resistance,  or  the  machine  is 
short-circuited,  the  amount  of  work  in  the  electric  cir- 
cuit of  the  machine  would  be  a  maximum,  and,  if  it 
could  be  reached,  would  be  expressed  by  the  formula, 

E* 

P  —  —  watts ;  where  E,  is  the  E.  M.  F.  generated  in  the 
r 

armature,  and  r,  is  the  internal  resistance  of  the  machine. 
This  activity  may  be  called  the  electric  capability  of  the 
machine,  and  is  similar  in  nature  to  the  electric  capability 
of  a  voltaic  cell.  Of  course,  no  machine  of  any  con- 
siderable size  could  be  made  to  run  on  short-circuit. 

136.  Since,  useful  output  can  be  computed  as  a  cer- 
tain fraction  of  the  electrical  capability,  depend- 
ing on  the  output  of  the  machine,  the  electrical  capability 
is  by  no  means  of  merely  theoretical  interest.     The  frac- 
tion of  the  electrical  capability  which   represents   the 
output  of  a  machine,  may  be  called  the  coefficient  of 
reduction  from  capability  to  output ',  and  varies  with  the 


132 


size  of  the  generator,  and  the  details  of  its  structure. 
For  example,  in  a  particular  series  of  bipolar  generators, 
of  different  sizes,  this  fraction  is  0.15  for  generators  of 
one  K.  w.  capacity,  and  reduces  to  0.034  for  generators 
of  100  K.  w.  capacity.  This  reduction  in  the  coefficient 
is  partly  due  to  the  fact  that  as  the  size  of  the  machine 
increases,  the  active  surface  of  the  armature,  offered  for 
the  dissipation  of  heat,  increases  less  rapidly  than  the 
mass  in  which  the  heat  is  developed,  thus  necessitating  a 
relatively  diminished  output. 

The  electrical  capability  of  a  generator  is  independent 
of  the  character  of  the  winding,  provided  the  amount 
of  winding  space  remains  constant.  This  is  true,  how- 
ever, only  so  long  as  the  proportion  of  winding  space, 
devoted  to  insulation,  remains  constant  through  all  sizes 
of  wire ;  thus,  if  the  number  of  turns  in  the  armature 
be  doubled,  the  E.  M.  F.  will  be  doubled,  but  the  resist- 
ance will  be  quadrupled,  since  there  will  be  twice  as 
great  a  length  of  wire  of  half  the  cross  section ;  hence 
the  ratio  of  E*  to  /*,  remains  the  same. 

137.     Since  the  E.  M.  F.  of  a  continuous  current  gene- 
rator is  proportional  to   0  n  w,  and  its  resistance 

is  proportional  to  —  2,  where  Z,  is  the  length  of  one  turn 
ct  p 

of  conductor,  «,  its  cross-section,  and  p,  the  number  of 
poles,  the  electrical  capability  of  a  machine  is  propor- 
tional to  <P*  n2  w2  °^  =  tf>*  n2  pz  — ,  that   is,  propor- 
w  I  I 

tional  to  C  ( — ^j-?\  .  where  (7,  is  the  weight  of  copper 
on  the  armature.  Consequently,  for  a  given  weight  of 


133 


copper  conductor  on  the  armature,  and  a  given  cross-sec- 
tion of  armature  core,  the  output  of  the  machine  in- 
creases as  the  square  of  the  speed  of  rotation,  and  as  the 
square  of  the  number  of  poles  in  the  field  frame.  Vari- 
ous considerations,  however,  incidentally  limit  the  range 
over  which  this  rule  can  apply.  Thus  an  increased 
capability  and  output  may  be  attended  by  increased  heat- 
ing or  sparking  at  the  brushes,  so  that  the  coefficient  of 
output  may  be  lowered.  A  doubled  speed  of  rotation 
would  double  the  E.  M.  F.  of  the  machine,  and  would 
quadruple  the  electric  capability,  enable  twice  the  cur- 
rent strength  to  be  delivered  at  full  load  at  the  same 
electrical  efficiency,  thus  quadrupling  the  output ;  but, 
if,  at  the  doubled  speed,  and  with  the  doubled  current, 
the  armature  unduly  heated,  the  safe  load,  and  coeffi- 
cient of  reduction,  would  require  to  be  lowered. 

138.  In  the  design  of  a  dynamo,  the  problem  which 
presents  itself  is  to  produce  the  desired  electro- 
motive force  at  a  given  speed  of  rotation  of  the  arma- 
ture, determined  by  mechanical  considerations,  and  to 
maintain  a  given  current  strength  at  that  E.  M.  F.  The 
problem,  therefore,  resolves  itself  into  the  proper  pro- 
portioning of  the  amount  of  flux,  the  number  of  turns 
and  size  of  conductor,  and  the  number  of  poles  in  the 
machine.  The  value  of  the  output  which  it  is  desired 
to  produce,  will,  in  reality,  determine  whether  the  ma- 
chine is  to  be  bipolar,  or  multipolar,  since  large  sizes  of 
bipolar  machines  are  usually  objectionable,  partly  owing 
to  the  large  dimensions  required.  Having  determined 
upon  the  number  of  poles,  the  total  flux  and  the  number 
of  turns  on  the  armature  only  remain  to  be  determined. 

The  proper  resistance  of  the  armature  for  the  type  of 


machine  required,  is  known  by  reference  to  tables  of  co- 
efficients for  the  electrical  capability  and  output,  and, 
from  this  resistance  one  relation  between  the  total  flux, 
the  length  and  the  cross-section  of  wire  is  given.  By 
trial  the  size  of  armature  is  found  upon  which  the 
amount  of  wire  of  the  necessary  cross-section  and  mun- 
.ber  of  turns  is  arrived  at. 

139.  The  magnetic  flux  requisite  under  a  given  con- 
dition of  speed  and  armature  turns,  now  remains 

to  be  provided  for.  The  first  step  is  to  provide  a  path 
of  sufficient  cross-sectional  area  through  the  iron  field 
frame  and  armature.  In  order  to  assign  the  proper  flux 
density  in  the  magnet  cores,  it  is  necessary  to  assume  a 
certain  quantity  of  leakage.  The  proportion  of  leakage 
is  generally  taken  from  observations  made  on  machines 
of  similar  type,  and  is  the  principal  source  of  uncertainty 
in  the  design  of  any  given  generator.  The  ratio  of  total 
flux  to  the  useful  flux  passing  through  the  armature 
varies  from  1.2  to  2.1  in  different  types  of  machine. 
When  this  ratio  is  known,  the  total  flux  passing  through 
the  field  cores  is  known,  and  the  area  of  cross-section 
necessary  for  a  given  flux  density  is  arrived  at. 

140.  It  will  be  seen  that  the  reluctivity  of  the  iron 
employed  in  the  framework  of  the  machine  is  a 

very  important  consideration,  since  on  this  depends  the 
area  of  cross-section  that  must  be  employed  for  a  given 
total  flux.  The  core  of  the  armature  is  always  con- 
structed of  a  given  quality  of  laminated  soft  iron,  with  the 
flux  passing  parallel  to  the  laminations.  The  field  mag- 
nets are  sometimes  entirely  constructed  of  cast  iron,  some- 
times of  cast  steel,  and  sometimes  of  wrought  iron  in 


135 


the  core,  united  with  cast  iron  iii  the  yoke.  The  choice 
of  materials  depends  upon  the  character  of  the  work  the 
generator  is  to  perform.  In  the  case  of  cast  iron,  a  flux 
density  of  7.5  kilogausses  is  approximately  the  practical 
limit,  while  in  wrought  iron,  or  cast  open  hearth  steel,  a 
density  as  high  as  17  kilogausses  can  be  employed.  The 
balance  of  advantage  lies  between  cost  of  materials  and 
limitations  of  size  and  weight. 

141.  Slight  impurities  in  wrought  iron  or  soft  cast 
steel  have  a  marked  influence  upon  their  reluc- 
tivity. The  most  common  impurities  in  iron  are  carbon, 
silicon,  sulphur,  phosphorus  and  manganese.  Of  these, 
carbon  produces  the  greatest  influence  on  reluctivity, 
and  taking  the  reluctivity  of  pure  wrought  iron  at  an 
intensity  of  7.5  kilogausses  as  0.0005,  the  influence  of 
small  quantities  of  these  impurities  on  the  reluctivity 
appear  to  be  expressed  as  follows:  Carbon,  0.25;  silicon, 
0.11;  manganese,  0.06;  phosphorus,  0.04,  and  sulphur, 
inappreciable. 

Thus,  one  per  cent,  of  carbon  added  to  pure  wrought 
iron  might  be  expected  to  increase  its  reluctivity  at  7.5 

kilogausses  from  0.0005  to  0.0005  +  0'2°  X  l  =  0.003; 

100 

i.e.,  to  three  rnillioersteds  in  a  cubic  centimetre  of  ma- 
terial. These  values  can  only  be  regarded  as  approxi- 
mations. They  appear  to  vary  in  different  qualities  of 
steel. 


136 


SYLLABUS. 

The  electromotive  force  produced  by  a  dynamo,  ex- 
pressed in  c.  G.  s.  units,  is  the  product  of  the  flux,  the 
revolutions  per  second  and  the  number  of  conductors 
counted  once  around  the  armature,  divided  by  the  num- 
ber of  poles.  The  electrical  capability  of  a  dynamo,  in 
watts,  is  equal  to  the  square  of  its  E.  M.  F.  in  volts, 
divided  by  its  resistance  in  ohms. 

The  ratio  of  the  total  to  useful  flux  varies  in  different 
machines  between  1.2  to  2.1. 

The  flux  density  that  can  be  employed  without  unduly 
increasing  the  reluctivity  of  the  circuit  is  about  7.5  kilo- 
gausses  in  cast  iron,  and  up  to  IT  kilogausses  in  wrought 
iron  or  soft  cast  steel. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER. ~| 
WEEKLY. 

No.  18.  OCTOBEK  13,  1894. 

Electrical   Engineering   Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED 

DYNAMO. 


142.  The  commercial  efficiency  of  a  dynamo-electric 
machine,  like  that  of  any  other  electric  source,  is 
the  ratio  between  the  output  and  the  intake,  and  varies, 
in  different  sizes  of  generators,  between,  say,  0.5  for  a 
one  KW.  machine,  to  0.98  for  a  generator  of,  say,  3,750 
KW.  In  other  words,  the  commercial  efficiency  of  a 

machine  is  OutPut  =  Intake-Losses^ 
Intake  Intake 

In  order,  therefore,  to  determine  the  efficiency  of  a 
machine,  the  intake  being  known,  it  only  remains  to  de- 
termine the  losses. 

These  are  of  three  kinds ;  namely, 

(1.)  Mechanical  losses,  such  air  churning,  brush  fric- 
tion, and  journal  friction. 

(2.)  Electrical  losses  of  the  type  $  r ;  namely,  losses 
in  the  armature  winding,  and  in  the  field  magnet  winding ; 
and  losses,  due  to  eddy  currents  set  up  in  the  metal  by 
variations  of  flux. 

(3.)  Magnetic  losses  in  the  iron  due  to  hysteresis. 

Published  by 

THE   ELECTRICAL  ENGINEER, 
203  Broadway,  New  York   N.  Y. 

[Entered  as  second  class  matter'at  the  New  York,  N.  Y.,  Post  Office,  June  14,  1894.] 


138 


143.  The  mechanical  losses,  as  a  rule,  are  readily  esti- 
mated. The  loss  by  air  churning  is  usually  small,, 
and,  in  large,  slowly  revolving  armatures,  may  be  neg- 
lected. Indeed,  a  small  expenditure  of  energy  in  this 
direction,  is,  to  a  certain  extent,  advantageous,  and  is 
sometimes  designedly  incurred  for  the  purpose  of  venti- 
lating the  armature,  and,  by  consequent  cooling,  increas- 
ing the  possible  output.  Brush  friction  is  usually  a  large 
item  of  loss  in  very  smill  machines,  and  an  insignifi- 
cantly small  item  in  large  machines.  Journal  friction 
can  be  readily  estimated  by  the  ordinary  rules  of  me- 
chanics, when  the  gravitational  and  magnetic  forces,  to- 
gether with  belt  pulls,  when  such  exist,  are  taken  into 
account,  together  with  the  size  of  the  shaft  and  length 
of  bearings. 


The  electrical  losses  of  the  type  i2  r,  are  of 
three  kinds  : 

First,  those  due  to  the  passage  of  the  armature  cur- 
rent through  its  resistance,  and  of  the  field  exciting 
current  through  the  resistance  of  the  field  magnets. 

Second,  those  due  to  the  energy  expended  by  waste- 
ful currents  in  loops  of  conducting  wire  on  the  armature, 
when  short-circuited  by  the  action  of  the  brushes  on  the 
commutator;  and, 

Third,  those  due  to  energy  expended  in  the  iron  of 
the  armature  or  pole-pieces,  or  in  the  copper  wire  on  the 
armature,  in  setting  up  induction  currents  in  them. 

145.     If  the  resistance  of  the  armature  of  a  100  KW. 

machine  be  0.05  ohm,  and  the  E.  M.  F.  of  the  ma- 

chine be  500  volts,  the  current  delivered  by  the  machine 

will  be  200  amperes.     The  electrical  loss  of  energy  in 


139 


the  armature  will,  therefore,  be  40,000  x  0.05  =  2,000 
watts  or  2  KW.  —  2  per  cent,  of  the  output. 

146.  If  the  armature  core  were  a  solid  mass  of  soft 
iron,  then,  from  the  variations  of  the  magnetic 

flux  produced  in  this  mass  during  its  revolution  through 
the  field,  E.  M.  F.'S  would  be  induced  in  it,  which,  acting 
through  the  very  low  resistance  of  so  large  a  mass  of 
metal,  would  generate  powerful  and  wasteful  currents. 
By  laminating  the  substance  of  the  core,  in  planes 
parallel  to  the  magnetic  flux,  the  E.  M.  F.  in  each  lamina 
is  reduced,  and  also  the  available  cross-section  for  the 
action  of  the  E.  M.  F.  By  thus  building  up  the  armature 
core  of  sheets  of  thin  iron,  the  eddy  current  loss  is 
brought  down  to  very  small  limits.  For  the  same  reason 
the  conducting  wire  on  the  surface  of  the  armature, 
when  of  comparatively  large  size,  needs  also  to  be  lami- 
nated by  stranding.  It  is  not  usually  necessary  to  insu- 
late the  separate  strands  from  each  other,  as  the  E.  M.  F. 
in  any  particular  cross-section  of  the  wire  is  so  small 
that  the  superficial  layer  of  oxide  of  copper  will  inter- 
pose an  effectual  barrier  to  the  passage  of  eddy  currents. 
When  the  conductors  are  buried  below  the  surface  of 
the  armature,  as  in  grooved  or  toothed  armatures,  lami- 
nation of  the  conductor  is  not  necessary,  since  the  flux 
is  almost  entirely  carried  by  the  iron  on  one  side  or  other 
of  the  conductor,  and  the  transition  is  effected  without 
cutting  the  substance  of  the  conductor. 

147.  The  third  source  of  loss  in   the  generator  is 
purely  magnetic,  and  is  termed  loss  by  hysteresis. 

Hysteresis,  meaning  a  lagging  behind,  is  the  lagging  of 
the  magnetism  in  a  magnetic  metal  behind  the_niagiietiz- 


140 


ing  flux  which  produces  it.  Thus,  on  the  reversal  of  the 
magnetizing  flux  exerted  on  a  piece  of  iron,  the  zero  of 
magnetism  is  reached  at  an  instant  of  time  sensibly  later 
than  the  zero  of  magnetizing  flux.  This  entails  an  ex- 
penditure of  energy  in  the  iron  which  takes  the  form  of 
heat. 

148.  If  an  electric  current  be  sent  through  a  con- 
ducting loop,  magnetic  flux  is  produced  through 
the  loop,  and,  during  the  time  the  current  strength 
is  rising  to  its  full  value  the  rate  at  which  flux 
is  entering  the  loop  will  induce  around  the  loop  an 
E.  M.  F.  of  the  type  e  volts.  This  E.  M.  F.  is  oppositely 
directed  to  the  current  i,  which  establishes  it,  and  con- 
sequently the  current  does  work  upon  the  E.  M.  F.  with 
an  activity  of  e  i  watts.  This  energy  is  stored  away  in 
the  air  and  the  ether,  as  magnetic  energy  of  the  type 

/ng 

—  ergs  per  cubic  centimetre.     On  withdrawing  the  cur- 

8  7T 

rent  and  emptying  the  loop  of  flux,  which  occurs 
during  the  time  the  current  is  waning,  an  opposite 
E.  M.  F.  is  produced,  aiding  the  current,  doing  work  on 
the  current  and  restoring  the  energy  from  the  magnetic 
flux  into  the  circuit.  This  interchange  of  energy  from 
the  circuit  to  the  ether  surrounding  it,  and  thence  back 
to  the  circuit  is,  so  far  as  is  known,  apart  from  electro- 
magnetic radiation  unaccompanied  by  loss  of  energy. 
If,  however,  a  bar  of  iron,  or  other  magnetic  material,  be 
introduced  into  the  loop,  then  the  magnetizing  flux  due 
to  the  current  passing  through  the  loop,  produces,  as 
before,  a  magnetic  flux  through  the  loop,  but  this  mag- 
netizing flux  acting  on  the  iron,  produces  by  the  align- 
ment of  its  molecules  a  powerful  M.  M.  F.  and  flux  in  its 


141 


own  direction.  As  before,  the  prime  flux  produces  a 
counter-electromotive  force,  0,  in  the  loop  absorbing 
energy  of  the  type  e  i,  joules  per  second.  The  flux 
passing  through  the  iron  and  loop  also  produces  a  more 
powerful  E.  M.  F.,  E)  volts,  absorbing  energy  from  the 
current  at  the  rate  E  i,  watts.  This  energy  is  stored  in 
the  magnetic  circuit  of  the  iron.  The  total  counter- 
electromotive  force  produced  will  be  E  +  0,  volts,  and 
the  work  expended 

r»T 

I      (E  -\~  e)  i  dt  joules. 
<J  o 

On  the  withdrawal  of  the  magnetizing  current,  the 
prime  flux  is  withdrawn  at  the  same  rate  as  before,  but 
the  magnetic  flux  in  the  bar  lags  behind ;  i.e.9  tends  to 
persist,  so  that,  although  the  current  in  the  loop  may  be 
made  to  disappear  entirely,  the  flux  in  the  aero-ferric  cir- 
cuit does  not  totally  disappear.  Consequently,  the  rate 
at  which  the  flux  is  poured  out  is  less  than  that  at 
which  it  was  poured  in,  and  the  smaller  E.  M.  F.  thereby 
induced,  restores  to  the  circuit  only  a  portion  of  the 
energy  stored  in  the  iron.  That  is  to  say,  the  lagging 
behind,  or  hysteresis,  of  the  magnetism  in  the  bar  has 
caused  energy  to  disappear  from  the  electric  circuit,  or 
to  be  lost  to  it. 

149.  Let  us  now  enquire  what  has  become  of  the 
energy  thus  lost,  to  the  circuit.  When,  under  the 
influence  of  the  prime  magnetizing  flux,  an  alignment 
of  the  molecules  of  the  iron  has  been  produced,  energy 
is  stored  in  them.  On  the  withdrawal  of  the  prime 
magnetizing  flux,  the  aligned  molecules  do  not  immedi- 
ately break  up  or  lose  their  alignment,  but  tend  to  re- 
main fixed  until  the  prime  magnetic  flux  is  sufficiently 


142 


far  withdrawn  to  render  tlieir  position  untenable.  They 
then  suddenly  break  up  their  alignment  and  fall  swiftly 
into  new  groups,  but  without  uniform  alignment.  In 


ETLUX 


(GAUSSES)  DENSITY 


FIG.  59. 

Hysteretic  Diagram  of  Charcoal  Iron  Rings  and  of  Hard  Cast  Steel. 

Charcoal  Iron: — Full  line  to  indicated  scale.  From  observations  of  Kennelly. 
«JC  ±  6,  OJ  ±  10,600. 

Hard  Cast  Steel: — Broken  line,  to  10  times  indicated  scale.  From  observations  of 
Steinmetz.  5C  ±  82,  (ft  ±  11,500. 


143 


this  sudden  relapse  to  the  unmagnetized  state,  the  mole- 
cules, in  swinging  around,  acquire  momentum  which 
carries  them  past  their  new  positions  of  equilibrium,  thus 
causing  them  to  oscillate  to-and-fro  about  that  position, 
and  to  dissipate  their  energy  in  the  form  of  heat. 

150.  The  magnetic  changes  which  take  place  in  their 
relation  to  magnetizing  flux  may  be  diagrammati- 

cally  represented  as  in  Fig.  59,  which  shows  a  hystere- 
tic  cycle  for  a  soft  iron  ring. 

151.  At  every  reversal  of  the  magnetization  of  the 
iron  there  is,  therefore,  an  expenditure  of  energy 

in  the  iron.  This  is  proportional  in  amount  to  the  area 
of  the  hysteretic  loop  or  the  energy  expended  in  the 
cycle.  As  the  limits  of  flux  density  during  the  reversal 
are  increased,  the  energy  expended  in  the  iron  increases. 
If  the  iron  be  carried  from  an  intensity  of  (B  =  -\-  5,00(  > 
gausses  to  (B  =  —  5,000  gausses,  the  range  of  reversal 
will  be  10,000  gausses.  If  now  the  range  be  doubled,  or 
increased  to  20  kilogausses,  the  energy  expended  in  the 
iron  per  cycle  will  be  approximately  trebled.  The  en- 
ergy expended  in  a  cubic  centimetre  of  iron  undergoing 
periodical  reversals  of  magnetism  is  approximately  ex- 
pressed by  the  equation  W  =  /?  (B1-6  ergs  per  c.  c.,  where 
rh  is  a  coefficient  which  varies  from  0.002  for  very  soft 
iron  to  0.080  in  the  hardest  steels. 

When,  therefore,  the  core  of  an  armature  of  soft  iron 
having  a  total  volume  of,  say,  8,000  c.  c.  makes  12  re- 
volutions per  second  in  a  bipolar  flux  from  (B  =  -|-  5,000 
to  —  5,000  gausses,  it  will  undergo  one  complete  cycle 
or  double  reversal  for  each  revolution.  Consequently 
the  expenditure  of  energy  in  the  core  by  hysteresis,  per 


144: 


revolution  of  the  armature,  will  be  0.002  X  SjOOO1-6  = 
0.002  X  828,600  =  1,657  ergs  per  c.  c.;  or  8,000  X  1,657 
=  13,256,000  ergs  —  1.3256  joules  per  revolution,  and 
at  12  revolutions  per  second  a  total  hysteretic  activity  in 
the  armature  of  15.907  joules  per  second  =  15.907 
watts.  For  this  reason  the  intensity  in  the  armature  is 
preferably  kept  much  below  saturation,  in  order  to  avoid 
the  rapid  increase  in  hysteretic  loss  at  high  densities  ac- 
cording to  the  above  rule. 

152.     If  the  three  classes  of  loss  of  energy  in  a  gene- 
rator be  summed,  their  total  subtracted  from  the 
intake,  is  equal  to  the  output,  and  this  divided  by  the 
intake  gives  the  commercial  efficiency  of  the  machine. 

SYLLABUS. 

The  losses  in  a  dynamo-electric  machine  are  three ; 
namely,  mechanical,  electrical  and  magnetic. 

By  hysteresis  is  meant  the  lagging  of  the  magnetiza- 
tion behind  the  magnetizing  force. 

The  loss  of  energy  in  a  magnetic  metal  undergoing  re- 
versals increases  approximately  as  the  1.6th  power  of 
the  limiting  flux  density. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.  1 
WEEKLY. 

No.  19.  OCTOBER  20,  1894. 

Electrical   Engineering  Leaflets, 


—BY— 

Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED 

THE  DYNAMO 


153.     The  limitations  to  the  output  of  a  dynamo  are 

of  three  kinds ;  namely,  limitations  by  excessive 

drop  or  fall  of  pressure  in  the  armature ;  limitations  by 

excessive  heatin  g;  and,  limitations  by  excessive  sparking. 

When  a  powerful  current  passes  through  the  armature 
of  a  generator,  the  fall  of  pressure,  or  drop  in  the  re- 
sistance of  the  machine,  may  be  so  great  that  the  limit- 
ing E.  M.  F.  developed  by  the  machine  may  not  be  capable 
of  supplying  at  its  terminals,  the  pressure  required  to 
operate  the  external  circuit.  This  limitation  exists  only 
in  the  case  of  small  machines ;  for,  provided  that  their 
normal  E.  M.  F.  has  been  correctly  apportioned,  large 
machines  find  their  limitations  in  other  directions. 

Limitations  due  to  excessive  heating  are  reached  when 
the  temperature  of  the  machine  acquires  a  certain  limit- 
ing or  critical  value.  The  heat  is  chiefly  developed  in 
the  armature,  where  friction,  hysteresis,  eddy  currents 


Published  by 

THE   ELECTRICAL  ENGINEER, 
203  Broadway,  New  Vork  N.  Y. 

[Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  June  14,  1894.] 


146 


and  resistance  losses,  that  is,  I2  7?,  losses  in  the  winding, 
due  to  the  load  current,  are  all  active.  ^  . 

154.  In  all  properly  drawn  contracts  for  installing 
generators,  the  specifications  require  a  certain 
limiting  temperature  elevation,  which  the  machine  shall 
not  exceed  after  a  certain  duration  of  continuous,  full 
load.  The  object  of  this  limitation  is  mainly  to  prevent 
such  a  rise  of  temperature,  on  any  part  of  the  machine, 
as  may  endanger  the  insulation  of  its  winding. 

Cotton  begins  to  char,  or  undergoes  slow  thermolysis, 
at  a  temperature  slightly  above  the  boiling  point  of 
water.  It  would,  therefore,  be  theoretically  safe  to 
operate  a  generator  at  continuous  full  load  with  the 
copper  wire  at  100°  C.  Taking  25°  C.  as  the  normal 
temperature  of  the  external  air,  this  would  represent  a 
temperature  elevation  of  75°  C.  Supposing  the  limiting 
current  of  a  generator  were  adopted  so  as  to  produce, 
after  continuous  full  load  run,  a  temperature  elevation 
of  75°  C.  in  the  factory •  in  cases  where  the  dynamo 
happened  to  operate  in  a  hotter  room,  say,  at  40°  C.,  the 
same  full  load  current  would,  probably,  raise  its  tempera- 
ture tP  115°  C.,  and  an  overload  under  such  circum- 
stances of,  say,  10  per  cent,  might  raise  it  to  125°  C. 
It  is  evident,  therefore,  that  a  due  regard  to  the  safety 
of  the  insulation  of  a  dynamo  requires  that  the  tempera- 
ture elevation  should  be  considerably  less  than  75°  C. 
The  temperature  elevation  frequently  met  in  conserva- 
tive specifications  is  40°  C. ;  in  special  cases  where  the 
generator  has  to  work  in  a  hot  room,  as  low  as  30°  C. 

155.     The  heat  developed  in  the  armature   of  a  gene- 
rator is  dissipated  by  conduction,   radiation  and 
convection.     The   usual   allowance   of   free   surface  in 


14T 


armatures  is  0.15  watt  per  square  centimetre,  but  when 
the  armature  is  specially  ventilated,  so  that  air  passes 
through  its  substance  as  well  as  over  its  surface,  this  may 
be  increased  to  as  much  as  0.45  watt  per  square  centi- 
metre. 

156.     Sparking  at  the  brushes  is  in  all  cases  the  result 

of  inductance.     That  is  to  say,  to  the  effect  of  an 

E.  M.  F.  produced  in   that  coil  or  section   of  winding 

which  is  leaving  contact,  through  its  commutator  seg- 

A 
c 


EUc.Engineer 

FIG.  60.  FIG.  61. 

Commutation    of    segments   on    the  Voltaic  circuit  made  up  of  single-volt 

Gramme -ring  armature.  cells.     Analogous  to  dynamo   armature 

Brushes  at  A  A',  15  volts  ;  BB',  13  volts; 
C  c',  ii  volts. 

ment,  with  the  brush.  If,  as  is  represented  in  Fig.  60, 
the  brush  H,  be  in  contact  with  the  commutator  bar  £, 
the  current  2  /,  flowing  through  the  brush,  will  be  made 
up  of  two  currents  each  equal  to  ./,  flowing  through  the 
adjacent  coils,  as  represented  by  the  arrows.  If  the  arma- 
ture revolves  counter-clockwise,  as  shown  by  the  arrow, 
then  the  relative  motion  of  the  brush  is  clockwise,  or  in  the 
opposite  direction.  If  the  width  of  the  brush  be  w  cms., 
and  the  width  of  the  gap  between  the  adjacent  bars  be  g 


148 


cms.,  then  the  distance  through  which  short-circuit  will 
be  maintained  between  two  bars  will  be  w  —  g  cms.  If 
a  be  the  radius  of  the  commutator,  its  circumference  will 
be  2  TT  0,  and  the  time  occupied  in  the  transfer  of  the 

brush  from  any  bar  to  the  next  will  be  s-  seconds. 

2  ii  n  a 

It  is  evident,  therefore,  that  the  current  in  the  winding 
section,  H,  must  be  stopped  and  reversed  in  this  fraction 
of  time  if  there  is  to  be  no  E.  11.  r.  between  J  and  H, 
when  H  is  transferred  to  <?,  and  taken  up  the  position  A. 
If  the  current  7,  in  the  segment,  B,  produces  indepen- 
dently of  the  flux  from  the  field  magnets  a  flux  <#, 
through  its  convolutions,  and  if  there  are  v9  convolutions 
in  this  section,  the  total  flux  linked  with  the  section  due 
to  its  own  current  will  be  v  0,  and  when  the  current  is 
reversed  to  —  /the  total  linked  flux  will  be  reversed  to 
-  v  ^ ;  the  total  change  will  be  2  v  <P,  and  the  time  in 

which  this  change  is  effected  w       ^  seconds,  so  that  the 

2  n  na 

average  E.  M.  F.  established  in  the  coil  during  the  change 

is  47rnav  ®  x  10-8  volts.     If  there  are   20  turns  of 
w  —  g 

wire  in  the  section  and  (P  =  10  kilowebers,  a  =  15  cms., 
n  =  12  revolutions  per  second,  w  —  g  =  1  cm.,  the 
average  E.  M.  r.  would  be : 

12.57  X 12  X 15  X  20  X  10,000  XlO~8  volts=4.525  volts. 
If  the  change  were  not  at  a  uniform  rate  during  the 
period  of  transfer,  the  E.  M.  F.  in  the  last  stages  would 
be  augmented,  and  might  rise  to  50  volts  or  more. 

157.     It  is  evident  that   <#,  depends  upon  the  output, 

while  V)  depends,  for  a  given  machine,  upon  the 

number  of  commutator  bars,  so  that  v  4>,  is  reduced  by 


149 


increasing  the  number  of  bars  in  the  commutator.  In- 
creasing this  number  up  to  a  certain  limit  diminishes  the 
E.  M.  F.,  or  sectional  E.  M.  F..  and,  therefore,  diminishes 
the  tendency  to  spark.  On  the  other  hand,  after  a  cer- 
tain limit  is  readied,  the  cost  of  construction  and  connec- 
tion of  the  commutator  increases  rapidly  with  the 
number  of  bars.  In  order  to  supply  the  E.  M.  F.  neces- 
sary to  comply  with  the  relations  indicated,  and  to  reverse 
the  current  in  the  short-circuited  segment,  it  is  usual  to 


PIG.  62. 

give  the  brushes  a  lead,  that  is  to  say,  to  move  them  for- 
ward in  the  direction  in  which  the  commutator  is  rotat- 
ing. The  lead  has  to  be  increased  as  the  load  increases, 
By  this  means  the  coil  under  commutation  is  brought 
within  a  portion  of  the  flux  from  the  field  magnets 
whose  variation  through  the  coil  supplies  the  E.  M.  F.  re- 
quired to  reverse  the  current  during  the  period  of  short- 
circuiting. 

Two  consequences  follow  a  lead  of  the  brushes  : 


150 


First,  the  reduction  of  the  E.  M.  r.  of  the  armature 
owing  to  the  position  and  consequent  neutralization  of 
some  of  the  $.  M.  F.  generated,  as  shown  in  Fig.  01. 

Second,  a  tendency  to  oppose  and  neutralize  the  con- 
trolling flux  through  the  field  magnets  at  the  pole  corner 
nearest  the  brush,  as  shown  in  Fig.  62. 

In  this  figure  the  normal  condition  of  the  flux  through 
the  pole-pieces  of  the  armature  of  a  four-pole  generator 
is  shown  at  the  quadrant  A,  when  no  current  flows 
through  the  armature,  the  direction  of  rotation  being 
indicated  by  the  large  arrow.  At  the  quadrant,  B,  the 
figure  represents,  diagrammatically,  the  flux  set  up  by 
the  M.  M.  F.  of  the  armature  winding,  in  the  quadrant 
under  A,  when  no  current  flows  through  the  same.  This 
M.  M.  F.  increases  with  the  load. 

At  the  quadrant  c,  the  effect  of  combining  or  super- 
posing these  two  conditions  is  similarly  represented,  and 
indicates  the  consequences  of  what  is  called  armature 
reaction  in  the  generator  under  load.  It  will  be  seen 
that  the  flux  is  crowded  together,  i.e.,  its  intensity  is  in- 
creased at  the  edge  of  the  pole  edge  6,  and  diminished 
under  the  edge  5. 

158.  The  magnitude  of  the  armature  M.  M.  F.  will  be 
1.25T  /  N  gilberts,  where  JT  is  the  number  of 
conductors  covered  by  a  pole-face,  and  7,  the  current  in 
the  winding,  and  this  will  be  almost  entirely  distributed 
in  the  two  air-gaps,  3  and  4,  or  5  and  6,  since  the  path 
through  the  iron  of  the  pole-pieces  and  armature  is  com- 
paratively short.  The  difference  of  maximum  difference 
of  magnetic  potential  across  each  of  these  air-gaps  will 

be  -    — _ —  gilberts ;  and,  if  the  entrefer  or  length  of 


151 


path  between  the  iron  and  iron,  be  f  cms.,  the  maximum 
possible  flux  density,  due  to  this  difference  of  magnetic 

1  257  I  N 
potential  will  be  — — -  gausses.      This   intensity  is 

opposed  to  the  controlling  intensity  in  the  entwefer  from 
the  field  magnets  at  the  edge  5,  and  added  to  it  at  the 
edge  6.  When  this  armature  intensity  is  equal  to  the 
intensity  from  the  field  magnets,  they  will  neutralize  and 
leave  no  intensity  at  the  edge  5,  while  the  intensity 
under  the  edge  6,  will  be  doubled.  When  the  neutrali- 


Elec.Engineer      ' 

FIG.  63. 

Section  of  one  Quadrant  of  a  4-pole  Generator  with  Tooth-cored  Armature. 

zatioii  is  effected,  no  amount  of  lead  can  be  of  any  ser- 
vice in  checking  sparking,  since  the  flux  whose  variation 
should  induce  a  controlling  E.  M.  r.  in  the  short-circuited 
segment,  lias  been  removed.  The  load  current  which,  in 
the  case  of  smooth-cored  armatures,  can  be  sustained 
without  sparking,  is,  therefore,  less  than  that  which  makes 

—p —  equal  to  the  intensity  in  the  gap,  when  no  cur- 
2  / 

rent  flows  through  the  armature,  and,  in  practice,  only 
about  half  this  limiting  current  strength  can  be  allowed. 


152 


159.  In  the  case  of  toothed  core  armatures,  such  as 
shown  diagrammatically  in  one  quadrant  by  Fig. 
63,  the  same  general  results  occur,  but  if  the  cross-sec- 
tion of  the  teeth  be  properly  designed,  they  will  suffice 
to  carry  a  normal  intensity  as  at  A,  in  Fig.  62,  without 
saturation  of  the  iron,  although  the  intensity  in  them 
under  this  action  may  be  high.  When,  however,  owing 
to  the  effect  of  the  M.  M.  F.  in  the  armature,  a  crowding 
of  the  flux  takes  place  towards  the  edge,  A,  this  tendency 
to  increase  the  intensity  saturates  the  iron,  and  enor- 
mously increases  its  reluctivity  in  the  teeth,  thereby  in- 
terposing a  barrier  to  the  distortion  of  the  flux,  and 
bringing  about  a  more  uniform  distribution  with  less 
reduction  of  flux  at  the  corner  B. 

For  this  reason  toothed-core  armatures  can  be  made 
to  sustain  greater  loads  than  prescribed  by  the  sparking 
limitations  of  smooth-core  armatures. 

SYLLABUS. 

The  limitations  of  a  dynamo  arise  from  the  drop  in  its 
armature,  from  excessive  heating,  or  from  excessive 
sparking. 

The  limitation  of  temperature  in  the  armature  of  a 
dynamo  is  imposed  in  order  to  prevent  the  possibility  of 
endangering  the  insulation  of  the  armature  by  excessive 
heating. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 
WEEKLY. 

No.  20.      :  OCTOBEB  87, 1894. 

Electrical   Engineering  Leaflets, 


—BY— 

Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED     GRADE. 

The  Regulation  of  the  Dynamo. 

160.  In  all  cases  where  more  than  a  single  receptive 
device  is  actuated  bj  a  generator,  some  means  are 

necessary  to  accommodate,  automatically,  the  output  of 
the  machine  to  changes  in  the  load.  If  the  recep- 
tive devices  are  connected  to  the  circuit  in  series,  and 
are  operated  by  a  constant  current,  it  is  necessary  to  in- 
crease the  E.  M.  F.  of  the  generator  in  proportion  to  the 
number  of  devices  thrown  into  the  circuit.  Such  are 
series-arc-light  generators  (see  Fig.  64).  If  the  devices 
are  connected  in  parallel,  and  are  operated  by  constant 
current,  the  voltage  at  each  device  must  be  maintained 
uniform,  and  the  current  and  pressure  of  the  machine 
varied  to  suit  this  requirement.  Most  continuous  cur- 
rent incandescent  generators,  are  of  this  type  (see  Fig.  65). 

161.  When  a  series-arc-light  generator  is  running  at 
a  constant  speed,  and  with  a  fixed  number  of 

turns  on  its  armature,  the  E.  M.  F.  developed  by  the  ma- 
chine can  only  be  varied  either  by  altering  the  quantity  of 

Published  by 

THE   ELECTRICAL  ENGINEER, 
203~Broadway,  New  York,  N.  Y. 

l[Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  Tune  14,  1894.] 


154 


flux  passing  through  the  armature,  or  by  varying  the  posi- 
tion of  the  brushes  on  the  commutator.  Fig.  61  indicates 
how  the  E.  M.  F.  of  a  generator  can  be  varied  by  chang- 
ing the  lead  of  the  brushes ;  except  that,  whereas,  in  the 
voltaic  analogue  represented,  the  coils  are  indicated  as 
having  the  same  E.  M.  F.,  the  coils  on  the  armature  of  the 
generator  have,  in  reality,  different  E.  M.  F.'S  existing  on 
opposite  sides  in  pairs. 

162.     In   most   arc-light  dynamos,  the  field  magnets 

are  connected  in  series  with  the  armature  which 

supplies  a  practically  constant  current,  and,  therefore, 


4- SUPPLY  MAIN 


-I- SUPPLY  MAIN 


Elec.  Engineer' 


FIG.  64. 

Series-wound  generator. 


SUPPLY  MAIN  Elec.Engiv 

FIG.  65. 

Shunt-wound  generator. 


the  M.  M.  F.  in  the  main  magnetic  circuit  is  practically 
constant,  and  the  entire  variation  of  E.  M.  F.,  say,  from 
50  to  3,000  volts,  is  provided  for  by  varying  the  posi- 
tion of  the  brushes  on  the  diameter  of  commutation 
from  the  diameter  of  minimum  E.  M.  F.  to  the  diameter 
of  maximum  E.  M.  F.  The  machines  are  so  designed 
that  the  M.  M.  F.  from  the  armature  winding  is  sufti- 

C5 

ciently  powerful  to  neutralize,  by  the  flux  it  produces, 
the  field  flux  through  that  portion  of  the  air-gap  and 
armature-surface  in  which  the  coils  undergoing  com- 


155 


mutation  are  situated,  in  the  manner  already  described 
in  Section  156,  so  that  the  commutation  is  practically 
sparkless  in  all  positions  of  the  brushes  within  regulat- 
ing limits.  If  this  balance  between  armature  and  field 
M.  M.  F.'S  and  flux,  were  not  maintained  throughout  this 
range,  violent  sparking  would  occur,  especially  as  arc 
light  machines  reach  such  high  pressures,  and  the  num- 
ber of  volts  per  bar  in  the  commutator  is  large. 

163.  "When  a  generator  running  at  a  constant  speed 
has  to  supply  a  varying  current  under  an  E.  M.  F. 

which  is  automatically  maintained  constant,  either  at  its 
own  terminals,  or  at  the  terminals  of  delivery,  a  com- 
paratively large  range  of  current  variation  has  to  be 
provided  for,  with  a  definite  but  much  smaller  range  of 
E.  M.  F.  variation.  Thus  a  100  KW.  generator,  intended 
to  supply  125  volts  at  its  terminals,  must  automatically 
maintain  a  pressure  of  125  volts  practically  constant 
under  all  conditions  of  load,  from  no  current  to  800  am- 
peres, the  E.  M.  F.  which  the  machine  must  generate 
being  in  one  case  125  volts,  and  in  the  other,  say,  130. 
This  variation  of  E.  M.  F.  of  five  volts  must  accompany 
the  increase  in  output  in  due  proportion.  In  such  cases 
the  variation  of  E.  M.  F.  is  obtained,  not  by  changing  the 
position  of  the  brushes  on  the  commutator,  but  by 
changing  the  M.  M.  F.  of  the  field  magnets. 

164.  If  the  magnetic  circuits  of  a  dynamo,  including 
the  leakage-  or  air-paths,  be  considered  as  analog- 
ous to  a  corresponding  system  of  voltaic  circuits,  as  re- 
presented, for  example,  in  Figs.  35,  42,  43  and  44,  each 
branch  reluctance  in  the  system  has  a  value  of  the  type 

-  (a  -\-  b  JC),  where  £,  is  the  virtual  or  real  length  of  the 


156 

branch  in  cms.;  s,  its  virtual  or  real  cross-section  in  sq. 
cms. ;  and  (a  +  I  5C)  its  reluctivity  at  the  prime  flux 
density  3C,  which  in  its  turn  may  be  considered  as  the 
average  magnetic  potential  difference  per  cm.  of  length, 
through  the  branch,  or,  if  37lb,  be  the  total  magnetic 

p.  D.  between  branch  terminals  -— b  =  mean  OC.    Under 

these  conditions  it  can  be  shown  that  the  flux  0a,  pass- 
ing through  the  armature  will  be 

d>    -=  ™  =  _      ^ 
a  ~~  (Ra  ~~  di  +  bi  9fTl ' 

so  that  the  apparent  reluctance  of  the  magnetic  circuit, 
considered  as  having  no  leakage  or  shunt  paths,  is  a 
linear  function  of  the  M.  M.  F.  in  which  a^  and  51?  are  con- 
stants depending  for  their  magnitude  upon  the  qualities 
of  the  iron  in  the  dynamo,  and  on  the  configuration  of 
the  magnetic  system.  This  relation  is  known  as 
Frolich's  law,  and  is  a  consequence  of  the  experiment- 
ally observed  fact  that  the  reluctance  of  any  branch  is 
constant  for  a  path  through  air,  and  of  the  form 


for  a  path  through  iron. 

In  computing  the  reluctance  in  the  magnetic  circuit  of 
a  dynamo,  a  slight  addition,  strictly  speaking,  is  necessary 
on  account  of  the  reluctance  of  such  joints  as  may  exist. 
It  has  been  found  by  measurement  that  the  reluctance 
of  a  joint  between  two  smooth  surfaces  of  wrought  iron 
is  equal  to  the  reluctance  of  an  air-gap  varying  from 
0.0026  to  0.0043  cm.  according  to  the  intensity  in  the 
iron  and  other  circumstances.  The  reluctance  of  a  well 


157 


fitted  joint  between  smooth  surfaces  of  soft  iron,  may, 
therefore,  be  estimated  as  0.003  oersted  divided  by  the 
area  of  the  joint  in  sq.  cms.  This  reluctance  will  usually 
be  a  negligibly  small  fraction  of  the  total  reluctance  of 
the  circuit.  The  reluctance  of  a  badly  fitted  joint  be- 
tween soft  iron  surfaces  may  however  be  considerable. 

165.  When  a  generator  has  its  load  increased  from 
no  load  to  full  current  load  of  7,  amperes,  the 
pressure  at  its  terminals  under  constant  M.  M.  F.,  diminishes 
by  I  R  volts,  7?,  being  the  resistance  of  the  generator. 
If,  in  addition  to  this,  a  lead  has  to  be  given  to  the  brushes 
to  maintain  sparklessness  at  the  commutator,  the  E.  M.  F.  of 
the  armature  will  be  diminished  by  an  amount  0,  volts, 
which  can  be  estimated  from  the  distribution  of  E.  M.  F. 
in  the  coils  around  the  armature,  but  which  is  almost  im- 
possible to  compute  accurately.  The  lead  of  the  brushes 
also  introduces  a  certain  small  counter  M.  M.  F.,  from  the 
armature  acting  through  the  main  magnetic  circuit  of 
the  field  coils,  thus  reducing  the  main  circuit  flux  and 
the  armature  E.  M.  F.  by  a  certain  small  amount  ei9  volts. 
The  problem  in  designing  an  automatic  constant  poten- 
tial generator,  is,  therefore,  to  cause  the  increase  of  cur- 
rent 7,  amperes,  which  tends  to  diminish  the  terminal 
pressure  by  the  amount  (7  R  +  0  +  <?i)  volts,  increase 
the  M.  M.  F.  of  the  field  magnets  to  the  extent  necessary 
to  increase  the  armature  flux  and  generated  E.  M.  F.  by 
this  amount. 

If  the  constants  av  and  51?  in  the  Frolich  equation 


«i  +  f>i  3ft 
were  known,  the  change,  A  2flt,  necessary  to  introduce  in 


158 


3fft,  for  the  required  change  in  0a,  would  be  immediately 
determined,  and  this  change  could  be  effected  by  causing 
the  load  current  /,  to  make  such  a  number  of  turns  t, 
around  the  field  magnets  in  aiding  the  shunt-winding,  as 
would  make  1.257  1  t  =  A  971.  The  machine  would 
then  be  compound-  wound  and  self-regulating;  i.e.^  would 
maintain  a  constant  M.  M.  F.  through  a  shunt-winding 
connected  to  its  constant  potential  terminals,  and  would 
develop  a  M.M.  r.  through  a  short  stout  winding  in  series 
with  its  armature.  This  auxiliary  M.  M.  F.  would  be 
zero,  at  no  load,  and  at  full  load,  would  reach  a  maxi- 
mum capable  of  compensating  for  the  tendency  of  the 
E.  M.  F.  to  fall. 

166.  In  practical  dynamo  magnetic  circuits,  however, 
owing  to  the  complexity  of  the  means  for  com- 
puting the  value  of  the  constants  a,  and  bly  it  is  prefer- 
able to  arrive  at  the  same  result  by  a  synthetic  process, 
as  follows  :  Having  given  a  total  fall  of  pressure  at  ter- 
minals due  to  full  load  under  a  constant  M.  M.  F.,  the  in- 
crease over  the  flux  through  the  armature  at  no  load, 
necessary  to  recoup  this  loss,  is  immediately  determined. 
The  intensity  in  the  armature  will,  consequently,  be  in- 
creased thereby  from  (Ba  to,  say,  &A,  and  the  reluctance 
of  the  armature  from 

CR,  =  A  /    _*        \  to  (RA  =       /  __  ^L^     oersteds, 
' 


,  =  A  /    _*        \  to  (RA  =  A  / 
*a\l  —  b&J'  sa\l 


a  and  5,  being  constants  for  the  quality  of  the  iron  in  the 
armature.  The  constant  reluctance  (R.K,  of  the  leakage 
paths,  placed  in  parallel  with  the  armature,  is  supposed 
to  be  known  from  the  type  of  machine,  from  previous 


159 


data,  or  from  direct  computation,  and  the  joint  reluc- 
tance of  the  armature  and  leakage  paths  will  be 

(ft,  =     ^^     oersteds. 
(RA  +  (RK 

The  total  flux  to  be  supplied  through  the  field  coil  or 
coils  must,  therefore,  be 


and  the  density  in  the  iron  of  the  field  magnets  becomes 

<*»  =  4, 

*M 

so  that  the  reluctance  of  the  field  cores  will  be 
-  l* 

-~ 


the  total  reluctance  in  the  circuit  will,  therefore,  be 

(R  =  (RK  +  CR,, 

and  the  M.  M.  F.  required  will  be 
371  —  </>M  (R. 

In  order  to  economize  the  extra  M.  M.  F.  required  to 
maintain  the  pressure  of  the  generator,  it  is  necessary  to 
keep  the  densities  (BA  and  (BVI,  well  below  the  limits  of 
saturation. 

167.  It  is  sometimes  required  to  maintain  the  pres- 
sure constant,  not  at  the  terminals  at  the  gene- 
rator, but  at  the  terminals  of  supply,  which  may  be  a 
mile  or  more  distant,  and  situated  at  a  real  or  virtual 
electrical  distance  r,  from  the  generator,  so  that  the 
drop  in  the  armature  and  supply  circuit  together  will  be 
[7  (R  -\-  y)  -f-  e  +  e?J  volts.  This  case  falls  iiumedi- 


160 


ately  into  the  preceding  treatment  by  supposing  the  re- 
sistance of  the  armature  increased  by  /•,  except  that  the 
shunt-winding  is  no  longer  maintained  at  uniform  ex- 
citation, but  slightly  increases  in  excitation  with  the 
load. 

In  order  to  make  up  for  any  deficiencies  in  design  of 
compound-wound  generators  so  as  to  permit  of  over- 
compounding,  resistances  called  compensating  coils  are 
sometimes  connected,  or  left  ready  to  connect,  in  parallel 
with  the  series-winding  on  the  magnets,  so  as  to  increase 
or  diminish  their  effect. 

SYLLABUS. 

Automatic  regulation  in  generators  is  employed  in 
practice  to  maintain  a  uniform  current  under  varying 
E.  M.  F.  or  a  uniform  E.  M.  F.  under  varying  current. 

Constant-current  generators  are  usually  regulated  by 
shifting  the  brushes. 

Constant-potential  generators  are  usually  regulated  by 
compound-winding,  that  is,  by  automatically  varying  the 
flux. 

Over-compounded  generators,  are  generators  whose 
compound  winding  is  designed  to  maintain  automatically 
a  constant  pressure  at  the  terminals  of  delivery,  instead 
of  at  the  terminals  of  the  generator. 

Laboratory  of  Houston  &  Keimelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELHCTRICAL  ENGINEER.] 
WEEKLY. 

No.  21.  NOVEMBEK  3,  1894. 

Electrical    Engineering   Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED     C  F?  A  D  E  . 

ELECTRODYNAMICS. 


168.  Electrodynamics  is  tliat  branch  of  electromag- 
netic science  which  treats  of  the  apparent  mutual 

attractions  and  repulsions  between  electric  currents,  or 
between  electric  currents  and  magnets.  The  apparent 
mutual  attraction  or  repulsion  between  magnets,  although 
frequently  classed  under  electrodynamics  more  properly 
belongs  to  the  separate  branch  of  imagnetodynamics. 

When  a  conductor,  situated  in  a  magnetic  flux,  has  a 
current  passed  through  it,  the  conductor  tends  to  move. 
This  tendency  to  motion  is  the  result  of  the  mutual  in- 
teraction between  the  flux  in  which  the  wire  is  situated, 
and  the  flux  produced  by  the  current  in  the  wire. 

169.  When  a  wire  of  length  /,  cms.,  Fig.  66,  situated 
in  a  uniform  flux  of  intensity  (B  gausses,  carries  a 

current  of  strength  i,  c.  G.  s.  units,  the  flux  surrounding  the 
wire  will  no  longer  be  represented  by  a  uniform  fleld,  but 
the  flux  above  the  wire  will  be  increased  in  intensity,  and 
the  flux  below  the  wire  decreased.  Under  these  circum- 


Published  by 

THE    ELECTRICAL   ENGINEER, 
20 1  Broadway,  New  York,  N.  V. 

[Entered  as  second-class  matter  at  the  New  York.  NT.  Y.,  Post  Office,  Tune  14, 


162 


stances  the  wire  will  be  forced  mechanically  towards  the 
side  on  which  the  flux  is  weakest,  and,  since  the  difference 
of  intensity  above  and  beneath  the  wire  depends  upon 
the  current  strength  through  the  wire,  the  electrodynamic 
force  with  which  the  wire  is  acted  upon  will  depend 
upon  the  current  strength.  The  value  of  the  force  ex- 
erted on  the  wire  will  be  f  =  i  (B  I  dynes.  It  is  evident 
that  if  in  obedience  to  this  force,  the  wire  is  moved  down- 
wards through  the  flux  with  a  velocity  v  cms.  per  second, 
the  E.  M.  F.  generated  in  the  wire  will  be  e  =  v  <B  / 


u 


FIG.  67. 


Diagram  of  rectangle  of  active  con- 
ductor A  B  c  D,  situated  in  a  uniform  mag- 
netic flux. 


c.  a.  s.  units,  as  already  shown  in  Sec.  124 ;  and,  since 
the  current  will  be  opposed  to  this  E.  M.  F.,  the  current 
will  do  work  upon  it,  and  energy  from  the  source  of 
current  will  be  expended  in  the  wire  at  the  rate  e  i  ergs 
per  second.  But  the  mechanical  activity  expended  on 
the  wire,  in  dynes,  will  be  the  force  on  the  wire  multi- 
plied by  its  velocity  in  cms.  per  second,  so  that  if/",  be 
the  force,  then 

f  i)  —  e  i      ergs  per  second, 

or,/  =  1*      dynes  =  v  (&U  ----  i  &  I       dynes. 


163 


The  force  exerted  upon  the  wire  will,  therefore,  de- 
pend upon  the  current  strength  through  the  wire  in  c.  G.  s. 
units,  (of  10  amperes  each),  on  the  intensity  of  the  flux, 
and  on  the  length  of  wire  in  that  intensity.  It  will  be 
moved  oppositely  to  the  direction  of  motion  which  would 
be  necessary  to  give  to  the  wire,  in  order  to  set  up  a  cur- 
rent in  the  direction  of  *,  by  induction  from  the  flux. 

170.  Fleming's  hand  rule  is  frequently  useful  for 
determining  the  direction  of  the  force  in  such 

cases.  But  it  must  be  remembered  that  the  left  hand 
is  employed  in  the  case  of  motors,  and  the  right  hand  in 
the  case  of  dynamos.  The  motor  rule  may  be  phrased 
as  follows.  If  the  hand  be  held  as  shown  in  Fig.  67, 
then  the /breflnger  represents  the  direction  of  the /lux, 
the  im'ddle  linger  represents  the  direction  of  the  current 
?",  and  the  thumb  points  out  the  direction  of  the  motion, 
or  tendency  to  motion,  produced  by  the  force. 

171.  We  have  seen  that  the  mechanical  force  exerted 
upon  an  active  conductor  in  a  flux  is  a  consequence 

of  the  law  of  the  induction  of  E.  M.  F.  in  such  a  wire, 
together  with  the  law  of  the  conservation  of  energy.  In 
order  that  a  conductor  may  carry  a  current,  it  must  form 
part  of  a  complete  loop  or  circuit,  and  the  total  mechan- 
ical force  exerted  on  a  conducting  loop  is  the  sum  of  all 
the  elementary  mechanical  forces  exerted  around  the 
loop  in  different  positions,  and,  perhaps,  in  different  in- 
tensities of  flux.  If  a  loop  carrying  a  current  of  strength 
?',  c.  G.  s.  units,  moves  under  mechanical  forces  in  any 
manner,  so  that  the  flux  linked  with  it  is  0,  at  any  mo- 
ment, the  E.  M.  F.  generated  in  the  loop  will  be  — —  ="  e, 

dt 


164 


c.  G.  s.  units,  and  the  work  done  on  that  E.  M.  F.  will  be 
e  i  ergs  per  second.  This  will  be  the  mechanical  activity 
expended  upon  the  loop  by  the  system  of  forces  at  work 
upon  it.  The  total  work  done  on  the  loop  from  the 
initial  position  it  occupied,  to  its  final  position  will  be 

C  e  idt  =  C^  idt  =  rid<P  =  i<P  ergs. 
Jo  Jo  dt  J  <P 

That  is  to  say,  the  total  work  will  be  the  total  increase 
of  flux  linked  with  the  circuit  multiplied  by  the  current 
strength  in  that  circuit,  or  the  total  increase  of  linked 
current-flux ;  and  this  work  is  independent  of  the  velocity 
at  any  stage  of  the  process,  or  of  the  manner  in  which 
the  motion  has  been  brought  about.  The  capability, 
therefore,  of  a  loop  to  do  work  by  motion,  depends  only 
on  the  total  flux  it  can  add  to  its  contents,  and  on  the 
strength  of  the  current  it  carries,  assuming  the  current 
strength  to  have  remained  constant. 

172.  It  is  evident  that  an  active  loop  always  endeavors 
to  move  so  as  to  add  as  much  flux  to  its  contents 
as  possible,  and  will  remain  in  stable  electromagnetic 
equilibrium  only  when  no  excursion  that  it  ca  make  will 
increase  the  flu  x  that  it  contains.  The  fundamental  reason, 
therefore,  for  the  mechanical  force  exerted  upon  an 
active  loop  is,  that  the  electromagnetic  energy  in 
the  ether  within  the  loop  tends  to  a  maximum.  That 

(B3 

energy  is  expressed  as  we  have  seen  in  Sec.  93  by  - 

8  x 

ergs  per  cubic  centimetre,  and  this  energy  in  the  space 
within  the  loop  can  only  become  a  maximum  by 
making  ®  a  maximum,  and,  therefore,  by  uniting  the 
direction  of  the  external  or  prime  flux,  with  the  direction 


165 


of  the  flux  produced  in  the  local  magnetic  circuit  of  the 
active  loop,  so  that  an  active  loop  will  tend  to  move  until 
its  own  flux  is  parallel  to  the  external  or  prime  flux,  i.e., 
the  flux  producing  the  motion. 

173.  The  key  to  all  the  phenomena  of  electro- 
dynamics may  be  expressed  as  follows  :  the  ten- 
dency of  the  electromagnetic  energy  in  the  ether  to  a 
maximum,  and,  consequently  the  tendency  of  fluxes  to 
become  parallel.  For  example,  consider  a  single  loop  of 
wire  A  B  c  D,  such  as  might  be  wound  on  a  drum  arma- 
ture of  the  bi-polar  electromagnetic  motor  shown  in  Fig. 
66.  Here  the  loop  contains  a  flux  of  its  own,  owing  to  the 
driving  current  supplied  to  the  motor,  and  this  flux  passes 
upwards  through  the  loop  as  shown  by  the  small  arrows. 
The  loop  immediately  tends  to  move  into  the  vertical 
position  in  which  it  will  hold  the  maximum  possible 
amount  of  flux. 

The  amount  of  work  which  will  be  performed  by  the 
loop  electrodynamically,  during  any  small  angular  move- 
ment d  /?,  is  i  d  0  ergs,  where  d  0  is  the  small  increase  of 
flux  admitted  into  the  loop  during  the  angular  movement 
d  /9.  This  work  can  also  be  expressed  as  r  d  ft  where  r 
is  the  torque  exerted  on  the  loop  about  its  axis,  so 
that,  equating  the  two  expressions  for  the  same  amount  of 

work,  r  d  ft  =  i  d  <P,  or  r  =  i  -^-^.      The    torque    ex- 

d  p 

erted  by  the  loop  is  therefore  proportional  to  the  rate  at 
which  a  small  angular  movement  will  increase  the  bi- 
polar flux  enclosed  by  the  loop,  and,  if  this  loop  existed 
on  an  armature  alone,  the  motion  would  cease  as  soon 
as  the  loop  reached  the  vertical,  where  the  flux  linked 
with  the  loop  is  a  maximum.  If  we  assume  that  at  some 


166 


point  in  the  plane  of  the  loop  A  B  c  D,  the  flux  due  to  the 
M.  M.  F.  of  the  loop  is  represented  in  magnitude  and 
direction  by  the  line  B  o,  Fig.  68,  and  the  external  flux, 
by  the  line  A  B  ;  then  at  this  point  the  resultant  flux  is 
A  c,  or  A  K.  When,  however,  the  loop  revolves  into  the 
vertical  position,  B  c  is  brought  to  B  D,  in  line  with  A  B, 
and  the  resultant  flux  density  at  the  point  is  A  D.  The 
voluminal  energy  in  a  cubic  centimetre  of  space  at  this 
point  being  proportional  to  the  square  of  the  density,  the 
increase  owing  to  the  re  volution  of  the  loop  is  proportional 
to  the  excess  of  the  area  A  F  G  D  over  the  area  A  E  H  K. 


r  £Uc.Engineer 

FIG.  68. 

Diagram  representing  the  increase  of  voluminal  magnetic  energy  in  space  effected 
by  the  alignment  of  two  independent  magnetic  fluxes. 

If  now  another  loop  be  added  to  the  armature  at  right 
angles  to  the  former,  and  also  traversed  by  the  driving  cur- 
rent, this  loop  will  be  at  its  position  of  maximum  torque 
when  the  first  loop  is  devoid  of  torque,  and,  if,  as  in  practice, 
the  number  of  loops  occupying  various  angular  positions 
be  placed  on  the  armature,  a  continuous  rotation  will  be 
effected.  Any  loop  reaching  the  vertical  position  abed, 
has  the  maximum  flux  linked  with  it,  and  would  tend  to 
resist  onward  movement  in  the  same  direction,  that  is,  it 


16T 


would  oppose  any  decrease  in  the  amount  of  flux  it  em- 
braces. Where  a  number  of  loops  are  placed  on  an 
armature,  in  order  to. render  the  motion  continuous  in  the 
case  just  supposed,  it  is  necessary  to  reverse  the  direction 
of  the  current  in  each  of  the  loops  when  they  have 
reached  the  vertical  position.  This  is  effected  by  means, 
of  a  commutator. 

174.  The  torque  of  a  motor  is  the  moment  of  the 
rotating  forces  about  the  axis,  and  is  equal  to  the 
virtual  tangential  force  exerted  at  unit  radius.  Thus,  if 
the  force  of  f  dynes,  has  to  be  exerted  tangentially  at  a 
radius  of  d  cms.  from  the  axis  of  a  motor,  in  order  to 
just  keep  it  from  moving,  the  starting  torque  of  the 
motor  is  F d  cm.-dynes ;  if  also  during  rotation  the  motor 
exerts  a  tangential  force,  say,  at  its  pulley,  of  500  Ibs. 
weight,  and  the  radius  of  the  pulley  is  1.5  feet,  the  run- 
ning torque  of  the  motor  will  be  750  foot-pounds. 

Since  the  torque  exerted  by  a  motor  armature  depends 
upon  the  intensity  of  the  flux  passing  through  its  loops, 
it  is  evident  that  doubling  the  intensity  of  the  flux  will 
double  the  torque;  consequently  the  object  of  iron  in 
the  armature,  is  to  enable  a  powerful  flux  and  flux  in- 
tensity to  be  maintained  through  the  armature,  from  the 
M.  M.  F.  in  the  magnetic  circuit  of  the  Held  magnets. 

SYLLABUS. 

The  cause  of  the  movement,  or  tendency  to  movement, 
between  active  neighboring  conductors,  or  between  active 
neighboring  conductors  and  magnets,  or  between  neigh- 
boring magnets,  is  a  tendency  of  voluminal  electro- 

(B2 
magnetic  energy  in  ether,  of  the  type  —  ergs  per  cubic 

8  7T 


168 


centimetre  to  a  maximum,  within  the  substance  of  mag- 
nets, and  within  the  interior  of  coils. 

In  order  to  produce  a  maximum  voluminal  electro- 
magnetic energy  in  ether,  fluxes  tend  to  associate  and 
unite  in  direction,  and  the  motion  or  tendency  to  motion ; 
i.e.,  the  force,  ceases,  when  parallelism  of  flux  is  attained. 

An  active  conductor  of  any  shape  tends  to  alter  its 
shape  in  such  a  manner  as  to  increase  the  flux  linked 
with  it,  i.e.  the  magnetic  energy  of  its  environment,  and 
the  force  so  exerted  ceases  when  the  flux  linked  with  the 
circuit  is  a  maximum. 

Loops  tend  to  become  circles,  and  coils  tend  to  shorten, 
magnets  to  approach  or  recede,  and  magnet  systems  to 
align  themselves,  in  obedience  to  these  laws. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 
WEEKLY. 


No.  22.  NOVEMBER  10,  1894. 

Electrical   Engineering   Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED     GRADE. 

THK  ELKCTRIC  MOTOR 

(CONTINUOUS    CURRENT   TYPE.) 


175.  We  have  seen  that  when  loops  of  wire  on  an 
armature  are  moved  through  a  magnetic  flux, 
supplied,  for  example,  by  field  magnets,  there  will  be 
E.  M.  F.  generated  in  the  loops  of  wire. 

We  have  also  seen  that  when  the  same  loops  of  wire 
carrying  a  current  are  placed  in  a  magnetic  flux,  there 
will  be  electrodynamic  forces  exerted  upon  the  loops. 

In  all  dynamo-electric  machines,  whether  dynamos  or 
motors,  both  these  conditions  necessarily  coexist;  that  is, 
in  the  dynamo,  the  generation  of  E.  M.  F.  is  necessarily 
accompanied  by  the  generation  of  electro-dynamic  forces 
as  soon  as  the  E.  M.  F.  drives  a  current  through  its 
circuit;  and,  in  the  motor,  the  generation  of  electro- 
dynamic  forces  is  necessarily  accompanied  by  the  gene- 
ration of  electromotive  forces.  In  the  dynamo,  the 
direction  of  the  electrodynamic  force  is  opposed  to  the 
direction  of  the  force  mechanically  exerted  on  the  ma- 
chine in  producing  its  E.  M.  F.,  while  in  the  motor,  the 


Published  by 
THE   ELECTRICAL   ENGINEER, 

203  Broadway,  New  York,  N.  V.  --f  f  TV  ¥1  T*  £  T  IH  ' 

[Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post     fftee,-  Jtirlfc  ij,  lift.]* 


QW   THIS 


170 


direction  of  the  E.  M.  F.,  generated  by  the  motion  of  the 
armature,  is  opposed  to  the  direction  of  the  driving  cur- 
rent. The  E.  M.  F.  of  the  motor  is,  therefore,  called  its 
counter •  E.  M.  F.  (abbreviated  c.  E.  M.  F.)  ;  and,  in  the  same 
way,  the  electrodynamic  force  of  a  dynamo  may  be  called 
its  counter  electrodynamic  force. 

1 76.  The  direct  E.  M.  F.  (abbreviated  D.  E.  M.  F.)  of  a 
generator  and  the  c.  E.  M.  F.  of  a  motor,  being 

similarly  produced,  are  subject  to  the  same  laws ;  conse- 
quently the  c.  E.  M.  F.  of  a  motor  is  expressed  by, 

e  =  0  n  w        c.  GL  s.  units, 

the  same  equation  as  in  the  case  of  a  generator,  where 
<P,  is  the  total  useful  flux  passing  through  one  pole  into 
the  armature  in  webers ;  n,  is  the  number  of  revolutions 
of  the  armature  per  second ;  and  w,  is  the  number  of 
conductors  lying  on  the  surface  of  the  armature,  counted 
once  entirely  around. 

From  the  identity  of  this  E.  M.  F.  equation  for  motors 
and  dynamos,  it  is  evident  that  if  a  motor  were  driven 
by  externally  applied  force  at  its  speed  n,  revolutions 
per  second,  but  without  receiving  any  driving  current, 
its  E.  M.  F.  as  a  dynamo,  would  be  equal  to  its  c.  E.  M.  F. 

177.  The  work  absorbed  by  a  motor  from  the  driv- 
ing circuit  will  be  e  i,  ergs  per  second,  where  *, 

the  strength  of  the  driving  current  in  c.  G.  s.  units  of 
10  amperes  each  =  i  (l>  n  w,  so  that  the  work  absorbed 
by  the  armature  during  each  revolution  will  be  i  0  w9  ergs. 

178.  The   preceding  considerations  render  manifest 
the  reversibility  of  all  continuous-current  dynamo 

electric  machines,  in  regard  to  their  generation  of  current 
by  motion,  or  their  generation  of  motion  by  current. 


171 


It  is  in  fact  well  known,  that  any  motor,  when  driven, 
will  act  as  a  generator,  and  produce  current,  provided 
its  field  magnets  are  capable  of  self -excitation,  or  are 
separately  excited ;  and,  similarly,  that  any  dynamo, 
when  properly  supplied  by  a  current,  will  act  as  a  motor 
and  exert  mechanical  force. 

179.  All  motors  are  required  to  produce  a  certain 
amount  of  mechanical  activity,  but  the  circum- 
stances under  which  this  activity  is  required  will  vary 
greatly  in  different  cases.     These  different  cases  may  be 
classed  as  follows ;  namely,  where  the  requisites  are, 

(1.)  Constant  torque  and  constant  speed. 

(2.)  Constant  torque  and  variable  speed. 

(3.)  Variable  torque  and  constant  speed. 

(4»)  Variable  torque  and  variable  speed. 

The  torque  and  the  speed  of  a  motor  are  its  essential 
features,  its  activity  being  the  product  of  the  two.  It 
will  be  necessary,  therefore,  to  examine  the  conditions 
which  determine  both  of  these  quantities.  If  r,  be  the 
torque  of  the  motor,  and  a>,  its  angular  velocity,  the 
activity  of  the  motor  will  be 

r  a)      ergs  per  second. 

The  angular  velocity  is  the  number  of  unit  angles,  or 
radians,  described  by  the  armature  per  second,  and  since 
there  are  ^  TT,  radians  in  each  complete  revolution, 

co  =  2  TT  n\ 

so  that,  the  activity  of  the  motor  is,  2  n  n  r  ergs  per 
second. 

180.  "We  have  already  pointed  out  that  the  torque  is 
the  mechanical  couple  exerted  by  or  on  a  motor,  or, 

its  tangential  force  at  unit  radius,  and  in  c.  G.  s.  units  at  a 


172 


radius  of  one  centimetre,  so  that  if  r,  dynes  be  exerted 
at  the  periphery  of  a  motor  shaft,  whose  radius  is  1  cm., 
the  work  done  in  one  complete  revolution  of  the  shaft 
will  be  2  TT  r,  ergs,  and  if  the  shaft  make  n,  revolutions 
per  second,  the  work  per  second,  or  activity,  will  be 
2  TT  n  r,  ergs  per  second,  as  before. 

For  example,  if  the  4-pole  shunt-wound  machine  repre- 
sented in  Fig.  58,  be  employed  as  a  motor,  instead  of 
as  a  generator,  its  activity  will  be,  say  100  KW.,  and  its 
commercial  efficiency,  0.9.  Then  the  electrical  activity, 
absorbed  by  the  machine  at  its  terminals,  will  be  J^-£-  — 
111.1  KW.  at,  say,  500  volts  pressure  and  222.2  amperes, 
of  which,  say,  218  amperes  pass  through  the  armature, 
and  4.2  amperes  through  the  field.  If  the  useful  flux 
through  each  pole  be  55  megawebers,  the  number  of 
wires  on  the  surface  of  the  armature  200,  and  the  resist- 
ance of  the  armature  0.05  ohm,  the  drop  of  pressure  in 
the  armature  at  full  load  will  be  i  r  =  218  X  0.05  = 
10.9  volts,  so  that  the  c.  E.  M.  F.  generated  in  the  arma- 
ture will  be  500  —  1  0.9  =  489.1  volts.  Since  e=  4>  nw, 

the  speed  .  =         = 


per  second,  or  266.7  revs,  per  minute,  or  an  angular 
velocity  of  4.445  X  6.283  =  27.93  radians  per  second. 
The  torque  of  the  motor  at  full  load  will  be 

r-P 

} 

CO 

where  P  =  the  mechanical  activity  of  the  motor  in 
ergs  per  second.  In  this  case  P  =  100,000  watts;  and 

one  watt  being  107  ergs  per  second,  r  =  =  3.58  X 

27.93 

1010  dyne-cms.  =  3.58  x  1.0203  X  1010  =  3.653  X  1010 


milligrammes  weight  (at  Washington)  3.653  X  104  kilo- 
grammes weight,  at  a  radius  of  one  centimetre. 

If  the  diameter  of.  the  pulley  were  30",  and  the  thick- 
ness of  the  belt  driven  by  the  pulley  f",  the  effective 
radius  of  transmission  —  ISf^"  or  46.2  cms.,  so  that  the 
effective  pull  exerted  by  the  belt 

=  3'653tx  1Q4  =  Y90.7  kilograinmes=1743  Ibs.  weight. 
46.2 

181.  When  a  continuous-current  shunt-motor  of  re- 
sistance /•,  ohms  with  separately-excited  field,  and 
whose  armature  is  ready  to  move,  is  connected  to  a 
source  of  constant  E.  M.  F.,  E,  volts,  a  current  will  now 
through  the  armature  of  the  motor  on  closing  its  circuit. 
The  strength  of  this  current  will  be  determined  not 
merely  by  Ohm's  law,  that  is  by  the  resistance  and  the 
E.  M.  F.  in  the  circuit,  but  also  by  the  inductance  of  the 
circuit,  which  tends  to  check  the  first  rush  of  current. 
The  initial  strength  of  current,  will,  therefore  be,  either 
equal  to,  or  less  than 

/*£ 

T 

The  torque  set  up  in  the  motor  by  this  current  will  be 

1  4>  w 

^r' 

and  if  this  torque  is  sufficient  to  set  the  armature  in 
motion  against  its  load,  the  armature  will  immediately 
start,  and  the  c.  E.  M.  F.,  generated  by  its  motion  will 
reduce  the  current  to  some  value  *,  expressed  by 

" 


r 
Under  the  influence   of  the   driving  current,  the  motor 


will  continue  to  accelerate  until  the  working  speed  is 
arrived  at,  which  satisfies  both  equations  of  energy  and 
of  E.  M.  F.;  for,  it  is  necessary,  that: 

First,  the  intake  is  equal  to  the  total  work  performed, 
or  that  e  i  =  speed  X  torque.  This  torque  includes 
not  only  the  mechanical  torque  usefully  exerted,  but  also 
the  f  rictional  torque  due  to  eddy  currents,  hysteresis  and 
journal  friction. 

In  well  designed  armatures,  employing  properly  lami- 
nated and  insulated  cores,  the  loss  of  power  in  eddy  cur- 
rents, and  the  torque  exerted  against  their  elect  rodynamic 
force,  are  comparatively  small.  The  torque  exerted  against 
journal  and  brush  frictions  may  be  approximately  deter- 
mined, when  the  motor  is  disconnected  from  its  circuit, 
by  ascertaining  the  smallest  weight  which  suspended  by 
a  cord  over  the  pulley,  will  maintain  the  armature  in 
motion.  This  weight  in  pounds,  multiplied  by  the  effec- 
tive radius  of  the  pulley,  gives  the  observed  frictiorial 
torque  in  pounds-feet.  A  torque  of  1  pound-foot  =  13,825 
gramme-cms.  =  13,550,000  dyne-cms.  (Washington.) 

As  soon  as  the  field  magnets  of  the  motor  are  sepa- 
rately excited,  the  torque  resisting  motion,  observed  in 
this  way,  will  be  found  to  have  considerably  increased. 
If  v,  be  the  volume  of  iron  in  the  armature  core  in  cubic 
centimetres  and  37,  its  hysteresis  coefficient,  (Sec.  151),  (&, 
its  maximum  intensity,  p,  the  number  of  field  magnet 
poles,  the  energy  expended  in  hysteresis  per  revolution 

of  the  armature  will  be  approximately  -JL-L  --    ergs, 

2 

and  the  torque   due   to  hysteresis  corresponding  to  this 


expenditure  of  work  will   be  -  dyne-cms.    Thus, 

4:  It 


175 


an  armature  of  a  4-pole  machine  (generator  or  motor) 
containing  120,000  c.c.  of  soft  iron  of  which  the  hyster- 
esis coefficient  is  0.002,  magnetizing  the  armature  at 
full  load  to  a  density  of  10  kilogausses  in  each  direction, 
would  exert  a  hysteresis  torque  resisting  motion,  of 

180,000  X4X  0.008X10,000"  =  mg  x  10,  dylMMang. 
12.5  1 

=  14.15  lbs.-feet. 

182.  Second,  the  pressure  at  the  terminals  must  be 
equal  to  the  c.  E.  M.  F.  plus  the  drop  in  the  arma- 
ture; or,  that^=  e-\-  ir.  The  speed  and  current,  there- 
fore, co-operate  to  satisfy  these  two  conditions,  and  these 
will  determine  the  normal  condition  of  operation  in  the 
motor  for  constant  excitation,  constant  pressure,  and 
constant  load,  the  total  activity  absorbed  by  the  armature 
being  E  i^  watts.  If  now,  the  load  on  the  motor,  i.e.,  the 
mechanical  torque,  be  increased,  the  speed  will  diminish 
and  witli  it  the  o.  E.  M.  F.  until  the  current  strength  in- 
creases to  a  value,  which  satisfies  both  the  energy  and 
pressure  equations. 

The  speed  at  which  the  motor  runs  is,  in  conformity 
with  these  conditions,  always  expressed  by  the  formula 

revs,  per  second. 


—  —  - 

0  w         W  w* 

The  first  term  gives  the  speed  at  which  the  armature 
would  run  if  it  had  no  drop,  and  the  second  term  gives 

the  rein  eta  nee  due  to  drop. 

^y^-^^j-JLU-^ff^ 
183.     It  is  evident,  therefore,  that  when  a  motor  is 

prevented  from  moving  by  excessive  torque,  it 
can  perform  no  useful  work,  because  its  c.  E.  M.  F.  would 
be  zero.  On  the  other  hand,  if  all  torque  could  be  re- 


1Y6 


moved  from  the  machine  its  speed  would  be  a  maximum, 
because  the  current  it  would  take  would  be  zero,  the 
maximum  activity  of  the  motor  existing  midway  between 
these  two  conditions ;  namely,  when  its  counter  E.  M.  F. 
is  half  that  of  the  pressure  at  terminals  or  equal  to  the 
drop.  This  would  be  represented  by  a  commercial  effi- 
ciency of  less  than  0.5.  In  practice,  however,  the  activ- 
ity of  all  motors  of  any  considerable  size  must  be 
considerably  greater  than  0.5,  for  the  reason  that  if  they 
were  to  expend  internally  half  the  energy  they  receive, 
they  would  become  violently  overheated. 

SYLLABUS. 

In  all  continuous  current  dynamo-electric  machines, 
whether  dynamos  or  motors,  E.  M.  r/s  and  electrodyna- 
mic  forces  are  developed.  In  dynamos  there  isacounter- 
electrodynamic  force  and  a  direct  E.  M.  F.  In  motors 
there  is  a  counter  E.  M.  F.  and  a  direct  electrodynamic 
force. 

Dynamos  and  motors  are  reversible  machines  when 
the  lield  magnets  are  capable  of  seif-excitation.  In  dy- 
namos the  E.  M.  F.  is  greater  than  the  pressure  at  the  ter- 
minals, and  in  motors,  the  c.  E.  M.  F.  is  less  than  the 
pressure  at  the  terminals,  by  the  amount  of  the  drop  in 
the  machine. 

The  controlling  factors  in  the  activity  of  motors  are 
the  torque  and  the  speed. 

A  torque  of  one  pound-foot  is  0.13825  kgm.-metre,  or 
13.55  megadyne-cms. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 
WEEKLY. 


No.  23.  NOVEMB.E  IT,  1894.       g*^^  Cent*. 

Electrical    Engineering   Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED     GRADE. 

THK  ELKCTRIC  MOTOR 

(CONTINUOUS    CURRENT   TYPE.) 


184.  When  a  motor,  connected  to  constant  potential 
mains,  is  loaded  witli  a  constant  torque,  there  are 

three  possible  ways  of  varying  its  speed  ;  viz., 

(1.)  By  shifting  the  brushes  on  the  commutator,  thus 
altering  the  amount  of  c.  E.  M.  F.  available  in  the  motor 
circuit. 

(2.)  By  inserting  a  resistance  in  the  armature  circuit, 
thus  producing  a  drop  of  pressure  in  the  circuit  of  the 
motor,  and  thereby  lowering  the  pressure  at  its  ter- 
minals. 

(3.)  By  varying  the  M.  M.  r.  of  the  field  magnets  of 
the  motor,  so  as  to  induce  a  varying  c.  E.  M.  F.  in  the 
armature,  forcing  it  to  alter  its  speed  in  order  to  main- 
tain a  constant  c.  E.  M.  F. 

185.  The  method  of  varying  the  speed  of  a  motor  by 
shifting  its  brushes  is  not  practically  employed ; 

since,  unless  efficiency  be  intentionally  sacrificed  in  the 
design  of  the  motor,  for  the  purpose  of  permitting  such 


Published  by 

THE   ELECTRICAL   ENGINEER, 
901  Broadway,  New  York,  N.  Y. 

[.Entered  as  second-class  matter  at  the  New  York,  N.  YM  Post  Office,  Juo«  14,  1894.] 


1Y8 


shifting,  violent  sparking  would  be  produced  at  the 
brushes. 

The  method  of  inserting  a  resistance  in  the  armature 
circuit  is  frequently  adopted,  especially  with  small 
motors.  It  is,  however,  a  wasteful  process. 

We  have  seen  that  the  torque  exerted  by  a  motor  is 

—  cm.-dynes,  (including  torque  against  friction)  so 

2  7t 

that,  the  torque  remaining  constant,  the  value  of  the 
driving  current  is  determined.  If  now,  the  speed  re- 
quired of  the  motor  is  such  that  the  c.  E.  M.  F.  (0  n  w) 
is  small,  the  difference  between  this  c.  E.  M.  F.,  and  the 
pressure  in  the  mains  must  be  made  up  of  drop  in  re- 
sistance i  r,  and  this  drop,  when  considerable,  will 
have  to  be  almost  entirely  produced  in  external  resist- 
ance. Calling  this  drop  <?,  the  activity  lost  in  heating 
the  external  resistance  will  be  e  i  watts,  which  will  be 
large  when  the  motor  is  running  slowly,  and  small  when 
it  runs  at  nearly  full  speed.  Moreover,  when  the  cur- 
rent *,  is  powerful,  and  the  drop  0,  is  large,  the  resistance 
must  be  constructed  in  such  a  manner  as  to  liberate  a 
large  amount  of  energy  without  overheating,  and  this 
necessitates  bulky,  cumbersome  and  expensive  rheostats. 

186.  The  third  method  for  varying  the  speed  of  a 
motor  under  constant  torque,  namely,  that  of 
varying  the  M.  M.  F.  of  the  iield  magnets  of  the  motor, 
though  frequently  employed,  is  necessarily  limited  in 
range.  Shunt  motors  can  have  their  M.  M.  F.  controlled 
by  means  of  resistance  inserted  in  the  circuit  of  their 
magnets.  The  range  of  variation  of  speed,  obtained 
in  this  way,  generally  amounts  to  about  25  per  cent. 
If  the  M.  M.  F.  of  the  magnets  be  reduced  beyond  a 


179 


certain  point,  the  armature  current,  which  has  to  be 
increased  in  order  to  maintain  a  constant  torque,  will  so 
far  increase  the  M.  M.  F.  of  the  armature,  as  to  destroy 
largely  or  even  to  overpower  the  field  flux,  and  thus 
give  rise  to  violent  sparking  at  the  brushes. 

187.  In  series  motors  the  variation  of  M.   M.  F.,  re- 
quired for  varying  the  speed,  is  usually  obtained 

by  commuting  the  field  coils ;  that  is,  by  arranging  the 
field-winding  into  a  certain  convenient  number  of  coils, 
and  connecting  these  coils,  by  a  suitable  device,  in 
series  or  parallel.  When  the  coils  are  all  in  parallel, 
their  united  M.  M.  F.  is  a  minimum,  and  the  speed  of 
the  armature  is  consequently  highest.  While,  when 
the  coils  are  all  in  series,  their  M.  M.  F.  is  a  maximum, 
and  the  speed  of  the  armature  consequently  least.  It 
is  undesirable  to  commute  the  field  coils  of  shunt  ma- 
chines, owing  to  their  large  inductance,  and  the  high 
pressures  that  may  be  excited  in  them  when  the  current 
strength  is  suddenly  altered  by  commutation. 

188.  It  is  possible,  under  extraordinary  conditions,  to 
obtain  a  shunt  motor,  of  say,  30  KW.  capacity, 

which  by  inserting  resistance  in  the  field  circuit,  and 
thus  varying  the  M.  M.  F.,  will  vary  its  speed  under  con- 
stant torque  and  constant  terminal  pressure  in  the  ratio 
of  3  to  1.  Under  usual  conditions,  however,  the  speed 
cannot  be  altered  in  this  way  in  a  higher  ratio  than  1.25. 
Series- wound  motors  can  be  controlled  in  speed  by  com- 
muting their  field-coils  in  a  ratio  of  from  1.25  to  2.0, 
depending  upon  the  amount  of  torque  exerted  by  the 
motor;  that  is,  upon  the  current  through  the  machine, 
and  the  reluctivity  of  the  iron  at  the  existing  M.  M.  F. 


180 


189.  The  condition  of  variable  torque  and  constant 
speed  is  commonly  met  with  in  operating  machin- 
ery, especially  machine  tools,  where  varying  loads  have 
to  he  encountered  at  constant  speeds.     A  series  motor, 
unless  specially  controlled,  is  unable  to  maintain  these 
conditions,  since  the  M.  M.  F.  is  constantly  varying  with 
changes  in  the  load. 

A  shunt  motor  would  maintain  a  constant  speed  under 
variable  torque,  up  to  full  load,  disregarding  the  modifi- 
cations induced  into  the  magnetic  circuit  by  armature 
reactions,  if  there  were  no  drop  in  the  armature  resist- 
ance. In  motors  of  between  3  and  50  KW.  capacity,  the 
armature  drop  averages  about  4  per  cent,  at  full  load, 
and  the  speed  will,  therefore,  alter  in  the  ratio  of  about 
1.04  between  light  and  full  loads.  This  is  usually  a  suffi- 
ciently close  regulation  of  speed,  but  it  is  possible  to 
employ  a  compound-wound  motor,  having  the  same  con- 
nections as  a  compound-wound  generator,  and,  therefore, 
so  arranged  that  the  armature  current  slightly  weakens 
the  M.  M.  F.  of  the  magnets,  thus  forcing  upon  the  arma- 
ture a  constant  speed  under  all  loads. 

190.  The  fourth  condition,  viz.,  that  of  variable  tor- 
que and  variable  speed,  is  best  exemplified  in  the 

case  of  the  electric  railroad  motor.  This  condition  is 
practically  met  both  by  the  insertion  of  resistance  in  the 
armature  circuit,  and  by  varying  the  M.  M.  F.,  of  the  field 
magnets,  which  are  usually  of  the  series  wound  type.  Such 
methods,  however,  while  they  may  satisfy  ordinary  re- 
quirements, are  far  from  being  a  complete  solution  of 
the  problem,  and  no  method  has  yet  been  introduced, 
which  can  accurately  control,  within  a  wide  range,  under 
variable  torque,  the  speed  of  a  motor  on  a  constant  po- 


181 


tential  circuit.  In  this  direction  the  capabilities  of  the 
electromagnetic  motor  appear  to  least  advantage. 

191.  When  a  shunt-wound   motor  has  to   be  started 
from  rest,  and,  therefore,  from  a   condition    of 

zero  c.  E.  M.  F.,  it  is  necessary,  since  the  resistance  of  a 
large  motor  armature  is  very  small,  that  the  terminals 
of  the  armature  should  not  be  directly  connected  to  the 
mains,  inasmuch  as  such  an  armature  connection  would 
practically  constitute  a  short  circuit  to  the  mains,  for  the 
tirst  rush  of  current  passing  through  the  armature  before 
its  inertia  can  be  overcome,  and  its  c.  E.  M.  F.  generated, 
may  be  sufficient  to  destroy  the  armature  winding1,  or  to 
injure  seriously  its  mechanical  construction. 

In  order  to  avoid  this  danger  it  is  usual  to  introduce  a 
resistance  called  a  starting  resistance  into  the  armature 
circuit,  by  the  drop  of  pressure  in  which,  the- pressure  at 
the  armature  terminals  may  be  correspondingly  reduced. 
As  soon  as  the  armature  is  sufficiently  accelerated  to  pro- 
duce a  suitable  c.  E.  M.  F.,  this  resistance  is  gradually  cut 
out  of  circuit,  thereby  causing  the  motor  to  still  further 
accelerate,  until  its  full  speed  and  c.  E.  M.  F.  are  attained, 
when  the  resistance  is  entirely  removed. 

192.  In   consequence  of  the  reversibility  of  a  gene- 
rator and  motor,  it  might  be   supposed  that  the 

output  of  a  dynamo-electric  machine  would  be  the  same, 
whether  employed  as  a  dynamo  or  as  a  motor.  This, 
however,  is  not  the  case,  since  in  a  generator  the  fric- 
tion losses  are  supplied  directly  from  the  engine,  while 
in  a  motor  they  have  to  be  supplied  from  the  driving 
current.  Suppose,  for  example,  that  a  generator,  sup- 
plies 100  amperes  at  100  volts  terminal  -pressure,  or  10 


182 


KW.  When  running  at  full  load,  its  loss,  expended  in 
friction,  of  say  2  KW.,  is  supplied  from  the  engine,  which 
delivers  12  KW.  to  the  generator  pulley.  If  the  machine 
be  driven  by  the  same  full  load  current  of  100  amperes 
as  a  motor,  and  with  the  same  terminal  pressure  of  100 
volts,  its  intake  will  be  10  KW.  and  its  output  say  8  KW. 


:oo 

WATTS.      INTAKE 


FIG  69. 


Curves  showing  Expenditure  of  Power  in   a  Half- Horse-Power  Series  Wound  Motor 
wound  for  500  volts. 

Owing  to  this  cause,  a  one  KW.  generator  will  be,  say,  a 
0.75  KW. 'motor,  or  practically  one  H.  p.,  but  a  large  gene- 
rator of,  say,  175  KW.,  might  be  a  160  KW.  motor. 

198.     Figs.  69  and  70  give  curves  taken  from  actual 

tests  of  a  well  known  type  of  motor  ;  Fig.  t>9, 

being  a  test  of  a  series-wound  £  H.  p.  motor,  and  Fig.  JO 


183 


a  corresponding  test  of  a  shunt-wound  machine  of  the 
same  make  and  power.  The  characteristic  properties  of 
shunt  and  series-winding,  in  regard  to  speed  and  effici- 
ency, are  clearly  shown.  The  loss  of  energy  taking 
place  at  all  activities  up  to  full  load  is  shown,  for  the 
Held  as  magnetizing  energy  (*' 2  /'),  for  the  armature  as 
drop  (i 2  r)  and  for  friction  of  eddy-current,  hysteretic 


0  100 

WATTS.      INTAKE 


FIG.  80 

Curves  showing  Expenditure  of  Power  in  a  Half-Horse-Power,  Shunt-Wound  Motor 
wound  for  500  volts. 

and  mechanical  types  combined.  Thus,  at  an  output  of 
850  watts,  the  shunt  motor  is  seen  to  have  absorbed  640 
watts,  of  which  82  were  expended  in  magnetizing  the 
field,  50  in  heating  the  armature,  and  the  remaining  158 
in  frictions,  representing  a  commercial  efficiency  of  54.0 
per  cent.;  while,  at  the  same  output  with  the  series  ma- 
chine, the  intake  was  620  watts,  with  57  in  the  field 


184 


magnets,  70  in  the  armature,  and  the  remainder  of  143 
in  frictions,  representing  a  commercial  efficiency  of  56.4 
per  cent.  The  speed  of  the  series  machine  drops  from 
38.5  revolutions  per  second  at  no  load,  to  21  revolutions 
per  second  at  full  load,  while  the  speed  of  the  shunt 
machine  drops  from  29.2  revolutions  per  second  at  no 
load,  to  25  at  full  load.  The  series  machine  is  somewhat 
cheaper  to  construct,  since  its  field  magnets  are  wound 
with  a  few  turns  of  coarse  wire  instead  of  many  turns 
of  finer  and  more  expensive  wire,  but  the  regulation  in 
speed  of  the  shunt  motor  is  much  closer. 

SYLLABUS. 

The  regulation  of  speed  in  a  motor  under  constant 
torque,  connected  to  constant  potential  mains  may  be 
obtained  either  by  inserting  resistance  in  the  armature 
circuit,  or  by  altering  the  M.  M.  F.  of  the  tield  magnets. 
This  variation  of  speed  is  practically  limited  in  range, 
and  constitutes  the  principal  disadvantage  of  the  electric 
motor. 

The  uniform  regulation  of  speed  in  a  motor  under 
variable  torque,  when  connected  to  constant  potential 
mains,  is  readily  obtained  either  by  shunt  winding,  or  still 
more  closely,  by  compound  winding. 

The  regulation  in  speed  in  a  motor  under  variable  tor- 
que, when  a  wide  range  of  speed  and  torque  have  to  be 
maintained,  is  accomplished  by  the  insertion  of  resist- 
ance in  the  armature  circuit  and  by  varying  the  M.  M.  F. 
of  the  n'eld  magnets,  whiclr  are  usually  series-wound. 

Dynamo-electric   machines    have,  other  things  being 
equal,  a  greater   output  when  employed  as  generators 
than  as  motors. 
Laboratory  of 'Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 
WEEKLY. 


Nn   94  "NViv^MRTTR  94-   18Q4-         Price,    -    10  Cents. 

S  J4,  1    M.        Subscription,  $3.00. 

Electrical   Engineering  Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED     GRADE. 

ELECTRIC  MOTOR, 

(CONTINUOUS    CURRENT   TYPE.) 


194.  Motor  armatures,  like  dynamo  armatures,  are 
either  smooth-cored  or  toothed-cored.  The 
toothed-cored  armature  was  one  of  the  earliest  forms 
devised.  Latterly,  however,  owing  to  its  mechanical  and 
electrical  ad  vantages,  the  toothed-cored  armature  has  again 
come  into  almost  universal  favor.  In  a  smooth-cored 
armature  the  electrodynamic  force  is  mainly  exerted  upon 
the  wires  on  its  surface  and,  therefore,  unless  these 
wires  are  very  carefully  bound  and  secured,  they  are 
liable  to  be  dislodged.  In  the  toothed-cored  armature, 
not  only  are  the  wires  more  completely  protected  from 
injury  and  in  a  position  more  favorable  to  complete  in- 
sulation, but  the  electrodynamic  force  is  no  longer  ex- 
erted upon  the  substance  of  the  copper,  but  on  the  mass 
of  the  iron  in  the  teeth.  The  M.  M.  F.  of  the  current  in 
the  wires,  affects  the  distribution  of  flux  from  the  M.  M.  F. 
of  the  field  magnets  through  the  armature  core,  and 
produces  a  distortion  of  flux  density  which  serves  to 


Published  by 
THE  ELECTRICAL  ENGINEER, 

203  Broadway,  New  York,  N.  Y. 

[Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  June  14,  1894.] 


186 


rotate  the  armature  according  to  the  law  of  tractive 
force,  ( —  dynes  per  sq.  cm.)  as  already  explained. 

\8  7T  / 

Moreover,  eddy  currents  are  avoided  in  the  substance  of 
the  conductor;  for  the  flux  no  longer  penetrates  the 
wires  themselves,  but  is  deflected  by  the  surrounding 
iron  either  to  one  side  or  to  the  other.  This  effect  does 
not  alter  the  E.  M.  F.  produced  in  such  imbedded  wires, 
since  the  rate  of  linking  flux  with  them  remains  equally 
effective  ;  and,  although  the  electrodynamic  force  set  up 
by  currents  in  the  wires  changes  its  point  of  application, 
yet  its  amount  is  unaltered. 

195.  The  effect  of  armature  reaction,  in  a  motor,  is 
the  same  as  in  a  dynamo,  except  that  its  relative 
direction  is  reversed  ;  that  is  to  say,  the  polar  edge  which 
is  weakened  is  the  trailing  pole,  or  the  pole  that  is  left, 
and  the  pole  which  is  strengthened,  is  the  leading  pole 
or  the  pole  that  is  approached.  This  is  evidently  owing 
to  the  fact  that,  other  things  being  equal,  the  current  in 
the  armature  is  in  the  reverse  direction  to  that  produced 
when  it  is  operating  as  a  dynamo,  and,  consequently,  the 
direction  of  the  armature  M.  M.  F.  is  reversed. 

Since  the  rotation  of  a  motor  is  produced  by  electro- 
dynamic  force,  the  leading  pole  requires  to  have  its  flux 
density  strengthened  by  armature  reaction,  and  the  fol- 
lowing, or  trailing  pole,  must  be  correspondingly  weak- 

(B2 
ened.     That  is  to  say,  the  distribution  of  -  — ,  is  such  as 

8    7T 

to  increase  at  the  leading  polar  edge,  in  accordance  with 
the  principles  described  in  Section  116,  so  that  the  arma- 
ture is  pulled  around  in  the  direction  of  the  denser  flux. 
In  a  generator,  however,  the  armature  has  to  be  moved 


by  mechanical  force  away  from  the  denser  flux,  at  the 

(B2 
strengthened   pole-piece  where  the  distribution  of   — 

is  greater,  and,  therefore,  the  trailing  polar  edge  is 
strengthened  by  armature  reaction.  Consequently,  the 
fact  that  the  direction  of  both  armature  reaction  and 
armature  M.  M.  F.  must  be  opposite  in  a  motor  to  that 
which  exists  in  a  dynamo,  is  the  fundamental  law  under- 
lying all  considerations  of  direction  of  relative  rotation 
in  motors  and  generators. 

196.  As  a  consequence  of  the  preceding  fundamental 
law,  it  will  be  seen,  that  in  order  to  preserve  the 
same  direction  of  rotation  of  the  armature  as  a  motor 
that  it  possesses  as  a  generator,  the  direction  of  current 
through  the  armature  must  be  reversed,  unless  the  direc- 
tion of  the  current  in  the  field  magnets  is  also  reversed. 
That  is  to  say,  the  relative  direction  of  M.  M.  r.  between 
field  magnets  and  armature  must  be  reversed. 

(1.)  Shunt-wound  machines  will  preserve  their  direc- 
tion of  rotation  as  motors,  either  when  the  current 
through  them  retains  the  same  direction,  or  when  the 
E.  M.  F.  at  their  terminals  retains  the  same  direction,  as 
in  their  condition  as  generators. 

(2.)  Series- wound  machines  will  reverse  their  direction 
of  rotation  as  motors,  either  when  the  current  through 
them  retains  the  same  direction,  or  when  the  E.  M.  F.  at 
their  terminals  retains  the  same  direction,  as  in  their 
condition  as  generators. 

(3.)  In  order  to  reverse  the  direction  of  rotation  of  a 
motor  it  is  necessary  to  change  the  M.  M.  F.  in  either  field 
or  armature ;  i.e.,  to  reverse  the  direction  of  either  the 
field  or  armature.  Merely  reversing  the  direction  of  pres- 


188 


sure  at  the  motor  terminals ;  or,  what  is  the  same  thing,  re- 
versing the  direction  of  current  through  the  entire  motor, 


DIRECTION  OF 
TERMINAL  CURRENT  PRESERVEI 


DIRECTION  OF 
TERMINAL  E.  M.  r.  PRESERVED 


GENERATORS 


Elec.Engin.eer 


FIG.  71. 

Showing  Relative  Direction  of  Rotation  in  Generators  and  Motors. 

does  not  change  its  direction  of  rotation  unless  the  ma- 
chine be   separately-excited.     These  relations  are  indi- 


189 


cated  diagram matically  in  Fig.  71,  where  the  uppermost 
row  of  machines  are  separately  excited,  the  middle  row 
are  shunt-wound,  and  the  lowest  row  series-wound.  The 
large  arrows  point  out  the  directions  of  M.  M.  F.  in  field 
and  armature,  and  the  curved  arrows  the  direction  of 
armature  rotation.  It  is  evident  that  in  order  to  retain 
as  a  motor  the  direction  of  rotation  possessed  as  a  dyna- 
mo, a  relative  reversal  of  M.  M.  F.'S  in  field  and  armature 
must  be  effected. 

197.  When  a  motor  is  connected  with  an  E.  M.  F., 
current  flows  through  the  motor,  and  electrody- 
namic  force  is  set  up,  as  we  have  seen,  between  the 
armature  and  field  fluxes.  Under  the  action  of  this 
force,  the  motor  accelerates  until  its  c.  E.  M.  F.  is  suffi- 
cient to  limit  the  current  strength  it  receives  to  the  amount 
required  for  the  performance  of  the  total  work  expended 
in  and  by  the  motor  at  the  speed  which  it  must  main- 
tain to  develop  that  c.  E.  M.  F.  When,  however,  two 
motors  are  connected  in  series,  they  will  tend  to  accele- 
rate, until,  by  their  united  c.  E.  M.  F.'S,  the  current  they 
receive  is  limited  to  the  total  work  they  absorb;  but 
since  by  varying  their  relative  speeds  the  same  amount 
of  c.  E.  M.  F.,  and  the  same  amount  of  work,  may  be 
distributed  between  them  in  an  indefinitely  great  num- 
ber of  ways,  it  is  clear  that  their  relative  speeds  will  be 
indeterminate.  For,  as  an  example  of  such  instability, 
consider  two  similar,  separately-excited  motors  A  and  B, 
to  be  connected  in  series,  and  each  loaded  by  indepen- 
dent, equal  and  uniform  torques,  such  as  by  weights  sus- 
pended over  their  pulleys.  Then,  for  a  given  current 
strength  passing  through  the  armatures,  by  symmetry, 
the  two  motors  will  run  at  equal  speeds,  dividing  the 


190 


total  voltage  equally  between  them,  and  exerting  equal 
activities.  But  any  slight  accidental  increase  in  the  tor- 
que imposed  on  one  motor,  say  A,  instead  of  automatically 
causing  an  increased  current  strength  from  the  mains  to 
overcome  the  extra  load,  might  be  met  by  the  absolute 
stoppage  of  A,  with  a  doubled  speed  on  the  part  of  its 
neighbor  B.  The  same  current  strength  would  continue 
to  flow  through  the  armatures,  but  one  motor  would  do 
all  the  work  and  generate  the  entire  c.  E.  M.  F. 

198.  For  the  same  reason,  motors  which  are  oper- 
ated in   series  arc  circuits,  are  difficult   to   con- 
trol  in   speed  unless   their    torque   increases  with   the 
speed,   as  in   the   case    of  fan   motors,  or  unless  some 
speed  governing   mechanism   is  employed   to   vary  the 
torque  in  relation  to  the  speed.     Few  motors  of  any  con- 
siderable size  are,  therefore,  operated  upon  series  circuits. 

It  is  often  necessary  in  practice  to  reverse  the  direction 
of  a  motor.  For  this  purpose  it  is  only  necessary  to  re- 
verse the  M.  M.  F.  either  of  the  field  or  of  the  armature. 
It  is  customary  in  such  cases  to  reverse  the  connections 
of  the  armature.  Care  lias  to  be  taken,  however,  not  to 
apply  too  powerful  an  F,.  M.  F.  at  the  brushes,  immedi- 
ately after  such  reversal ;  for,  the  c.  E.  M.  F.  of  the  arma- 
ture, which  will  be  still  revolving  by  its  momentum  in 
the  original  direction,  will  now  be  an  E.  M.  F.  in  the 
same  direction  as  the  driving  current,  and  will,  therefore, 
aid  in  producing  a  very  powerful  current  through  the 
armature,  which  may  act  as  a  short  circuit  on  the  mains. 

199.  Whatever    may   be   the   importance   of    small 
weight  in  the  case  of  stationary  electric  motors, 

there  can  be  no  doubt  that,  in  the  case  of  electric  loco- 


191 


motors,  it  is  desirable  to  reduce  their  weight  for  a  given 
output  as  much  as  possible.  For  a  given  output  the 
torque  required  may  vary  within  wide  limits,  and  is  in- 
versely as  the  maximum  speed  the  motor  has  to  main- 
tain. When  a  motor  can  produce  a  given  output,  it  is 
evident  that  any  torque  can  be  theoretically  obtained  from 
it  by  sufficiently  increasing  or  reducing  the  speed  of  rota- 
tion through  the  necessary  gearing.  In  practice,  however, 
such  gearing  is  frequently  objectionable  from  the  fric- 
tion, noise  and  wearing  introduced  by  it.  Thus,  street- 
car motors  as  first  employed,  reduced  their  speed  of 
rotation  by  double  gearing  from  12  to  25  times,  accord- 
ing to  the  type  and  power  of  motor  employed.  They 
now  usually  reduce  their  speed  by  single  gearing  from 
four  to  five  times,  requiring,  however,  a  slower  armature 
speed  and  a  greater  corresponding  torque  for  the  same 
output ;  or,  in  other  words,  a  more  powerful  motor.  By 
employing  cast  steel,  multipolar,  field  magnets,  and  by 
economy  in  weight,  street  car  motors  are  built  which  de- 
velop at  their  armature  shafts  a  torque  of  133,000  dyne- 
cms.,  per  ampere,  per  kilogramme,  that  is  0.00448  or 
212-5  pound-foot,  per  ampere,  per  pound  of  total  motor 
weight,  not  including  the  weight  of  gearing ;  so  that  at 
this  rate,  a  500-volt  motor  weighing  223  pounds,  and 
supplied  with  one  ampere,  would  exert  a  torque  of  one 
pound-foot.  A  500-volt  stationary  motor  of  about  the 
same  size  (15  H.  p.)  usually  exerts  a  torque  at  its  arma- 
ture shaft,  of  about  0.001  to  0.0015  pound-foot  per  am- 
pere, per  pound  of  weight,  so  that  street-car  motors  are 
usually  about  four  times  more  powerful  than  stationary 
motors  in  reference  to  their  weight. 


>       Of 

UNIVERSITY 


192 


SYLLABUS. 

In  smooth-cored  armatures,  the  electrodynamic  force 
is  largely  exerted  upon  the  substance  of  the  conductors 
wound  upon  its  surface,  but  in  toothed-cored  armatures, 
the  armature  is  sheltered  from  both  eddy  currents  and 
from  electrodynamic  force  by  the  surrounding  iron. 

In  a  generator,  the  leading  polar  edge  is  weakened, 
while  in  a  motor  it  is  strengthened  by  armature  M.  M.  F. 
and  reaction ;  consequently,  the  M.  M.  r.  in  a  motor  arma 
ture  must,  for  the  same  direction  of  rotation  be  reversed 
in  direction  to  that  which  existed  in  a  generator. 

Motors  operated  in  series,  are  unstable  in  speed  unless 
their  torques  are  either  maintained  in  uniformity,  or  in- 
creased at  a  greater  ratio  than  their  speeds. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 
WEEKLY. 


No.  25.  DECEMBEK  1,  1894. 

Electrical   Engineering  Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED     CRADE. 

ELKCTRIC   HBATINQ. 


200.  When  an   electric   current   of  strength  i,  ex- 
pressed in  c.  G.  s.  units,  passes  steadily  through  a 

resistance  of  r  c.  G.  s.  units,  a  c.  E.  M.  r.  of  e  =  i  r  c.  G.  s. 
units  is  developed  in  the  resistance,  while  energy  is  ex- 
pended by  the  current  against  this  c.  E.  M.  F.,  at  the  rate  of 
e  i  =  i2  r  ergs  per  second,  and  appears  in  the  resistance 
as  heat.  Transformed  into  practical  units,  a  current  of  i 
amperes,  passing  steadily  through  a  resistance  of  r  ohms, 
develops  a  c.  E.  M.  r.  of  i  r  volts,  and  does  work  at  the 
rate  of  one  joule  per  second  (10  megergs),  or  with  an 
activity  of  one  watt,  as  heat  in  the  resistance. 

201.  The  scientific  unit  of  heat  generally  employed 
is  the  amount  of  heat  required  to  raise  the  tem- 
perature of  a  gramme  of  water  from  3°  to  4°  C.     This 
unit  is  indifferently  called  the  lesser  calorie,  the  therm, 
the  gramme-calorie,  or  the  water-gramme-degrce-centi- 
grade. 

Since  the  calorie  is  not  a  c.  G.  s.  unit,  it  is  more  con- 

Published  by 

THE  ELECTRICAL  ENGINEER, 
303  Broadway,  New  York,  N.  Y. 

[Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  June  14,  1894.] 


194 


venient,  in  electrical  engineering,  to  employ  as  the  prac- 
tteal  unit  of  heat,  its  mechanical  equivalent  ;  namely,  the 
joule,  or  10  megergs.  The  joule  is  equivalent  to  0.23D 
therifi  ;  or,  in  other  words,  4.18  joules  approximately  are 
required  to  be  expended  in  heat  to  raise  the  temperature 
of  one  gramme  of  water  one  degree  C.  (One  British 
Thermal  Unit,  or  B.  T.  u.,  that  is,  1  pound  of  water  raised 
from  68°  to  69°  F.,  requires  an  expenditure  of  1053 
joules,  so  that,  roughly,  1  B.  T.  u.  =  1  kilojoule). 

Heat  produced  in  resistance  by  electrical  currents  is 
either  purposely  developed,  as  in  electric  heaters  or  elec- 
tric furnaces,  or  incidentally  and  unavoidably  developed, 
as  in  dynamo  machinery  and  wires  conveying  currents. 

202.  The  flow  of  heat  through  a  conductor  follows 
the  same  law  as  that  which  determines  the  flow  of 
electricity  through  a  conductor,  i.  e.,  Ohm's  law.  If  6, 
be  the  difference  of  temperature  in  degrees  Centigrade, 
between  two  parallel  plane  surfaces  of  the  conductor, 
and  xSr,  the  thermal  resistance  of  this  portion  of  the  con- 
ductor, then  H,  the  strength  of  the  thermal  current,  in 
joules  per  second,  will  be 


$,  is  determined  as  follows  ;  viz.,  if  y,  be  the  thermal  re- 
sistivity, Z,  the  length  of  the  conductor  in  cms.,  and  «, 
its  cross-sectional  area  in  square  centimetres,  then 

#=*-£. 
a 

The  thermal  resistivity  of  a  substance  is  the  reciprocal 
of  its  thermal  conductivity,  and  may  be  defined  as  being 
equal  to  the  reciprocal  of  the  amount  of  heat,  expressed 


195 

in  joules,  which  will  traverse  a  cube  of  the  material  one 
cin.  in  length  of  edge,  in  one  second  of  time,  with  1°  C. 
difference  of  temperature  between  two  opposed  faces. 

Thus,  if  a  wire  had  a  resistance  when  heated  to  100° 
C.  of  1.41  ohms,  and  was  enclosed  in  a  cubical  box 
whose  internal  edge  was  10  cms.  in  length,  with  walls 
composed  of  felt  and  1  cm.  thick,  the  external  surface 
being  zinc  lined,  and  maintained  by  immersion  in 
water,  at  a  temperature  of  20°  C.,  then  if  the  wire  were 
so  disposed  within  the  interior  that  its  temperature 
was  immediately  communicated  to  the  internal  surface 
of  the  walls,  these  would  each  have  a  cross-section  of 
100  sq.  cms.  and  a  difference  of  temperature  of  80°  C. 
between  the  inner  and  outer  surfaces.  The  thermal  re- 
sistivity of  felt,  expressed  in  c.  o.  s.  units,  according  to 
the  above  notation  is  about  2750,  so  that  the  resistance 

1   V  2750 

of  each  wall  Avould  be  — - — : —  =  27.5,  and  since  the 

1UO 

box  has  six  walls,  the  total  thermal  resistance  would  be 
^2.  =  4.583.  The  flow  of  heat  would,  therefore,  be 

80 

=  17.46  joules,  and  the  current  strength  which 
4.583 

would  have  to  be  sent  through  the  wire  to  maintain  its 
temperature,  with  that  of  the  interior  walls,  at  100°  C., 
would  be  1.41  X  i2  —  17.46,  or  i  =  3.52  amperes. 

The  preceding  relations  form  the  basis  for  determining 
the  amount  of  energy  required  to  be  expended  in  obtain- 
ing a  fixed  temperature  in  a  closed  electric  stove  of  given 
dimensions  and  material,  after  due  allowance  has  been 
made  for  the  thermal  capacity  of  the  contents ;  i.e.,  of 
the  amount  of  heat  required  to  be  expended  in  such 


196 


contents  in  order  to  raise  them  initially  to  the  required 
temperature. 

203.  The  following  is  a  list  of  thermal  resistivities 
for  a  few  substances.  These  values  can  only  be 
regarded  as  approximations.  Comparatively  few  obser- 
vations have  been  made,  and  the  thermal  resistivity  of  a 
substance,  like  its  electric  resistivity,  varies  both  with  its 
physical  condition  and  with  its  temperature. 

Like  electric  resistivities,  it  would  seem  that  good 
thermal  conductors  conduct  better,  and  good  thermal 
insulators  insulate  better  at  low  temperatures. 

THERMAL  RESISTIVITIES  IN  JOULEAN  UNITS. 


THERMAL  CONDUCTORS. 

Silver 0.17 

Copper 0.225 

Zinc 0.81 

Brass 0.83 

Iron 1.52 

Lead 1.95 

German  Silver 2.29 

THERMAL  INSULATORS. 

Stone 50 

Chalk. .  100 


Glass  .....................  100 

Sand  .....................  300 

Gutta-percha  .............  500 

Caoutchouc  ..............  600 

Clay  .....................  800 

Sawdust  ..................  2000 

Wool  ......  -  ..............  2100 

Paper    ...................  2200 

Vulcanized  Indiarubber.  ...  2700 


Felt. 


2750 


204.  In  general,  heat  developed  in  a  conductor  by 
the  passage  of  an  electric  current  is  dissipated  by 
conduction,  radiation  and  convection.  The  conduction 
losses,  as  we  have  seen,  depend  both  upon  the  dimen- 
sions and  thermal  resistivity  of  the  conducting  substance, 
and  the  difference  of  temperature  at  opposing  surfaces. 
The  loss  of  heat  by  radiation  follows  less  simple  laws, 
and  the  loss  of  heat  by  convection  is  still  more  complex. 


197 


205.  Radiant  heat  is  believed  to  be  a  purely  electro- 
magnetic phenomenon,  and  its  laws  are  not  yet 

accurately  known.  The  rule  commonly  employed  in  com- 
puting the  amount  of  radiation  from  a  hot  body  is  an 
empirical  rule  determined  by  Dulong  and  Petit  from  a 
large  number  of  practical  observations :  The  loss  by 
radiation  is  proportional  to  the  surface  of  the  heated 
body,  to  the  nature  of  the  surfaces  of  surrounding  bodies, 
arid  is  in  geometrical  proportion  to  the  absolute  tempera- 
ture of  the  surfaces.  The  loss  of  heat  from  a  body  by 
convection  depends  upon  the  temperature  of  the  surface 
of  the  body,  the  nature,  and  density  of  the  surrounding 
medium,  the  normal  amount  of  motion  in  the  medium 
(for  instance,  wind  in  the  case  of  air)  and  the  form  of 
the  body,  with  the  friction  which  its  surface  offers  to 
the  motion  of  the  medium.  The  result  is  a  complex 
thermodynamical  and  hydrodynamical  problem  which 
has  only  been  reduced  to  quantitative  results  in  a  very 
few  cases. 

206.  Although  radiation  from  the  surface  of  the  hot 
wire  takes  place  in  geometrical  proportion  to  its 

temperature  elevation,  yet  it  is  usually  sufficient,  within 
the  range  of  ordinary  temperatures,  to  take  a  mean 
value  of  the  radiation  in  direct  proportion  to  the  rise  of 
temperature. 

One  sq.  cm.  of  bright  copper  radiates  0.0006  watt  per 
C°  temp,  elevation  (approximately). 

One  sq.  cm.  of  blackened  copper  radiates  0.001  i  watt 
per  C°  temp,  elevation  (approximately). 

For  practical  purposes  the  convective  loss  of  heat 
from  a  wire  supported  horizontally  in  still  air,  may  be 
taken  as  independent  of  the  diameter,  and  as  equal  to 


198 


0.00175  watt  per  linear  cm.  of  the  wire  per  °C.  of  temp, 
elevation  (0.0533  watt  per  foot).  In  moving  air,  as  for 
example,  in  ordinary  weather  out  of  doors,  the  convec- 
tive  loss  is  usually  many  times  greater. 

20Y.  The  temperature  elevation  of  a  wire,  for  a 
given  current  strength,  depends  upon  its  resistivity, 
diameter,  covering  and  environment.  A  bare  wire  is 
best  cooled  by  supporting  it  on  insulators  in  the  open 
air,  where  any  breeze  or  other  motion  of  the  air  that 
may  exist,  will  carry  off  its  heat  convectively.  A 
covering  of,  say,  cotton,  rubber,  or  other  electric  non- 
conductor will,  up  to  a  certain  thickness,  serve  to  cool 
the  wire  by  increasing  its  surface,  even  although  the 
thermal  resistivity  of  such  materials  is  very  high.  A 
buried,  insulated  wrire  is  usually  kept  much  cooler, 
by  conduction  through  the  substance  of  the  soil,  than 
the  same  wire  suspended  in  quiescent  air;  while  an 
insulated  wire,  submerged  in  water,  is  maintained  still 
cooler,  by  reason  of  rapid  convection  of  heat  through 
the  water  together  with  its  large  thermal  capacity. 

The  following  table  gives  the  diameter  of  copper 
wire,  required  to  carry  the  various  current  strengths, 
with  an  elevation  of  20°  0.  in  temperature,  as  deduced 
from  actual  measurements  of  the  heating  of  wire  under 
different  conditions.  If  the  normal  temperature  of  a 
wire  be  30°  C.,  the  continued  passage  of  the  tabulated 
current  strength  will  cause  the  wire  to  approximately 
attain  the  temperature  of  50^  C.,  which  will  enable 
the  wire  to  be  held  in  the  hand  without  pain,  and 
such  a  temperature  may  be  considered  as  a  safe  limiting 
temperature.  Fire  insurance  rules  both  in  the  United 
States  and  in  Great  Britain  require  a  lower  temperature 


109 


elevation  and  limiting  current-strength  in  order  to  pro- 
vide a  margin  of  safety,  namely,  what  is  equivalent  to 
an  elevation  of  10°  C.  at  full  load,  or  about  33  per  cent, 
less  current  strength. 

TABLE  OF  DIAMETERS  OF  COPPER  WIRE,  OF  CONDUCTIVITY  98  PER 
CENT.  MATTHIESSEN'S  STANDARD,  ELEVATED  20°  C.  BY  VARIOUS 
CURRENT  STRENGTHS  ix  AMPERES  (ALTERNATING  OR  CON- 
TINUOUS). 


Effective 
Current 
Strength 
Amperes. 

Covered  Wire 
in  Wooden 
Moulding. 

Bare  Wire  Suspended 
Horizontally  in  Still  Air 
Within  Doors. 

Bright.             Blackened. 

Bare  Wire  Suspended 
Horizontally  in  Calm 
Weather  Out  of  Doors. 

Bright.            Blackened. 

Inches. 

Inches. 

Inches.                Inches. 

Inches. 

5 

O.020 

0.015 

0.014                      o.on 

0  010 

10 

0.036 

o  030 

O.O28                              O.O22 

0.020 

15 

O.OJ2 

0.045 

0.042                              0.032 

0.030 

20 

0.069 

0.060 

0.057                              0.042 

0.039 

25 

0.085 

0.075 

0.068                              0.052 

0.049 

3° 

O.IOO 

0.090 

0.080                     0.061 

0.038 

35 

0.114 

0.103 

0.092                     0.070 

0.066 

40 

0.127 

0.115 

0.105                     0079 

0074 

45 

0.140 

0.128 

0.117                     0.087 

0.082 

So 

0.152                      0.140 

0.130                     0.094 

0.089 

60 

o  175 

o.i  68 

o  152                     0.108 

o  103 

70 

0.197 

0.190 

0.171                                 O.I22 

olu6 

So 

0  2l8 

O.2I2 

O.I92 

0.134 

0.128 

9° 

0.236 

0.235 

O.2iO 

0.146 

o  140 

100 

°.-<54 

0257 

0.227 

0-157 

0.151 

I25 

O.2Q2 

0.307 

0.265 

0.183 

0.175 

150 

0.326 

°-365 

0.308 

O.21O 

O.2O2 

175 

°-357 

0.410 

o-347 

0.234 

o  227 

200 

0.386 

0.450 

0-385 

0.256 

0.248 

250 

0.440 

0.520 

0-455 

0.299 

O.2yO 

300 

0.615 

0.518 

0-339 

0-330. 

400 

0.765 

0.640 

0.418 

0.406 

500 



o  910 

0.750 

0.488 

0.471 

600 

.... 

0.857 

0-550 

0-533 

700 

.... 

0.958 

o.6n 

o-593 

800 

.... 

.... 

0.671 

0.650 

goo 

.... 

.... 

.... 

0.717- 

0.693 

IOOO 

.... 

0.782 

0-745 

200 


208.  The  rapid  elevation  of  temperature  in  an  over- 
loaded conductor  is  practically  employed  in  safety 
fuses  which  are  formed  of  high  resistivity  conductors 
with  a  small  surface  per  unit  length  and  a  low  melting 
point,  so  that  an  excess  of  current  strength  above  their 
rated  capacity  readily  fuses  them.  The  heat  developed 
in  a  safety  fuse  depends  upon  its  resistivity  at  the  work- 
ing temperature,  on  the  current  strength,  and  on  the 
length  of  the  fuse.  As  the  current  strength,  and  con- 
sequently the  temperature,  increases,  the  resistivity  of 
the  metal  increases,  the  energy  expended  in  unit  length 
increases,  and  the  rate  of  dissipation  of  the  energy  by 
conduction,  radiation  and  convection  also  increase  until 
the  melting  temperature  is  attained.  Except  in  fuse 
wires  of  very  small  diameter,  the  predetermination  of 
their  melting  current  becomes  very  complex  and  differ- 
ent under  different  circumstances,  such  as  the  inclination 
of  the  fuse,  its  surface,  condition,  etc.  With  large  fuses 
the  capacity  for  heat  may  be  such  that  an  enormous  over- 
load may  be  safely  carried  for  a  very  brief  interval,  the 
energy  being  expended  in  raising  the  temperature  of  the 
metal  while  a  much  smaller  steady  increase  of  load 
would  certainly  melt  them. 

SYLLABUS. 

Heat  escapes  from  a  hot  body  by  conduction,  radiation 
and  convection.  Conduction  follows  a  law  similar  to 
Ohm's  law.  Radiation  is  believed  to  be  a  purely  elec- 
tromagnetic function  of  the  ether  and  follows  laws  not 
yet  fully  ascertained.  Convection  is  a  still  more  com- 
plex function  depending  upon  the  material  environment 
of  the  body. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 
WEEKLY. 

No    2fi  DT?mr\rRT?p  8    1  8Q4-         Price»     '    10  Cents. 

^  X    **•        Subscnption,  $3.00. 

Electrical   Engineering   Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED     GRADE. 

LIGHTING 


209.  AVhen  a  substance  is  lieated  to  the  temperature 
of  incandescence,  it  imparts  energy,  by  wave  mo- 
tion or  radiation,  to  the  surrounding  ether.     This  wave 
motion  comprises  a  great  variety  of  vibration  frequencies. 
All  waves  of  frequencies  lying  between  the  limits  of  ap- 
proximately 390  trillions  and  760  trillions  per  second,  are 
capable  of    affecting  the  eye  as   light.     All  radiations 
whose  frequencies  lie  outside  these  limits,  since  they  fail 
to  affect  the  eye  are  called  non-luminous  or  obscure  radi- 
ations.    Of  the  radiant  energy  emitted  by  a  body,  only 
a  certain  quantity  consists  therefore  of  luminous  energy. 

210.  If  w,  be  the  activity  of  radiation  per  unit  dif- 
ference of  frequency,  the  total  luminous  activity 

can  be  expressed  as, 

760,000,000,000,000 

y-» 
w  dn  watts, 

390,000,000,000,000 

where  n,  is  the  frequency.     This   is  shown  in  Fig.  72, 

Published  by 

THE  ELECTRICAL  ENGINEER, 
203  Broadway,  New  York,  N.  Y. 

[Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  June  14,  1894.] 


202 


which  roughly  represents  the  distribution  of  radiant 
activity  with  reference  to  the  frequency  of  vibration  in 
an  ordinary  incandescent  lamp.  The  frequencies  com- 
prised between  the  ordinates  e  Jc  and  g  h,  are  luminous 
frequencies.  The  shaded  area  e  f  g  h  #,  comprised  be- 
tween the  curve  and  base,  between  these  limits,  repre- 
sents the  number  of  watts  expended  by  the  lamp  in 
luminous  radiation.  The  unshaded  areas  represent  the 
non-luminous  activity.  The  ratio  of  the  shaded  to  the 
unshaded  area  is  about  0.03. 


X10 


FlG.    72 

Distribution  of  radiant  energy  from  incandescent  filament  with  respect  to  vibration 
frequency. 

Area,  e  f  g  h  k  =  luminous  activity  in  watts. 
Curve,  A  B   c    =  physiological  coefficient  of  illuminating  power   referred  to  standard 

frequency  as  unity. 
Area,  E  F  G  H  K  =  effective  physiological  illuminating  power. 

The  total  flux  of  radiation  activity  emitted  by  a  fila- 
ment of  surface-area,  S  sq.  cms.  at  an  absolute  temperature 
T,  is  expressed  by 

P  =  TcSTeaT  watts, 

where  k,  is  a  constant  depending  upon  the  nature  of  the 
filament,  and  a  =  0.0043. 

The  luminous  effect  produced  on  the  average  normal 
eye  by  a  given  quantity  of  radiation  activity,  say  one 
watt,  is  not  the  same  in  different  parts  of  the  spectrum ; 


203 


that  is,  at  different  frequencies.  For  the  average  eye, 
the  maximum  effect  is  produced  in  the  yellow,  at  a  fre- 
quency of  about  500  trillions  per  second.  The  amount 
of  illuminating  power  in  a  given  source  of  light  cannot 
therefore  be  determined  from  the  total  activity  of  radia- 
tion. It  becomes  necessary  to  determine  the  illuminating 
values  of  one  watt  of  activity  at  all  frequencies  within 
visual  limits.  If  this  physiological  coefficient  of  illumi- 
nation be  expressed  by  z,  in  suitably  chosen  units,  or,  as  in 
Fig.  72,  by  reference  to  the  physiological  effect  B  D,  at  some 
standard  frequency,  taken  as  unity,  then  the  illuminat- 
ing value  of  any  quantity  of  energy  w  dn,  covering  a 
small  range  of  frequency  dn,  will  be  z  w  dn,  and  we 
obtain  by  the  application  of  the  coefficient  z,  a  new 
curve  E  F  G  H  K,  whose  area  is 

7.6  XlO14 

w  dn 

3.9  XlO14 

units  of  physiologically  effective  illumination.  For  this 
reason  it  is  impossible  to  compare  accurately  the  illumi- 
nating power  of  two  different  sources  of  light,  such  as  a 
candle  and  an  arc  light,  unless  the  physiological  coeffi- 
cient 2,  at  present  undetermined,  be  known  for  all  parts 
of  the  spectrum,  as  well  as  the  distribution  of  activity  in 
the  spectra  of  the  two  sources. 

211.     The  most  efficient  source  of  light,  if  it  could 
be  produced,  would  be  that  in  which  all  the  en- 
ergy radiated  possessed  a  frequency  within  visual  limits. 
Considering  illuminating   power   alone,  that  particular 
frequency  near  which  2,  is  a  maximum,  that  is  some- 

<2*Uir&^T^ 

where  near  the  ^cHow  of  the  spectrum,  would  be  the 
most  advantageous  frequency  the  source  could  possess, 


204 


but,  considered  with  reference  to  fitness  for  agreeable 
illumination  and  the  distinction  of  colors,  that  distribu- 
tion of  frequencies  would  be  the  most  desirable  which 
best  agreed  with  the  distribution  in  sunlight. 

212.  The  frequencies  which  are  predominant  in  the 
radiation  of  bodies  heated  to  incandescence,  are 
non-luminous  frequencies.  Consequently,  in  all  artifical 
sources  of  illumination,  the  larger  proportion  of  the  en- 
ergy radiated  is  of  a  useless  character.  It  has  been  found 
that,  in  the  neighborhood  of  1 ,000°  C.,  as  the  temperature 
of  a  luminous  body  increases,  the  luminous  radiation 
rapidly  increases,  so  that  the  attainment  of  a  very  high 
temperature  is  essential  for  a  successful  artificial  illumi- 
nant.  A  high  refractory  power  is  necessary,  therefore, 
to  sustain  the  high  temperature  required,  and  carbon  is 
the  only  common  substance  which  has  yet  fully  met 
this  requirement.  An  illustration  of  the  importance  of 
a  high  temperature,  and  the  efficiency  of  luminous  radi- 
ation, is  seen  in  the  case  of  the  arc  and  incandescent 
lamps,  each  of  which  employ  incandescent  carbon  as  a 
source  of  radiant  energy,  but  in  the  arc  lamp  the  tem- 
perature attained,  being  that  of  the  volatilization  of  car- 
bon, is  higher  than  that  which  the  incandescent  filament 
can  safely  and  continuously  sustain.  The  amount  of 
energy  expended  in  an  arc  lamp  is  usually  about  450 
watts,  and  of  this  about  eight  per  cent,  is  expended  in 
luminous  radiation,  the  balance  being  non-luminous,  while 
in  incandescent  lamps  the  percentage  of  luminous  radia- 
tion is  about  three.  Moreover,  the  distribution  of  energy 
differs  in  these  two  sources  of  light,  the  average  physio- 
logical coefficient  being  greater  in  the  spectrum  of  the 
arc  lamp,  than  in  the  spectrum  of  the  incandescent  lamp. 


205 


213.  The  object  in  the  commercial  incandescent  lamp 
is  to  produce  an  electrically  heated  incandescent 
surface  at  the  highest  practical  temperature ;  for,  as  we 
have  seen,  such  a  temperature  will  produce  the  best  effi- 
ciency of  luminous  radiation  and  a  fair  approximation 
to  the  character  of  sunlight. 

The  high  temperature  necessary  for  the  proper  work- 
ing of  an  incandescent  lamp  must  be  uniformly  main- 
tained over  the  entire  surface  of  the  filament,  and,  to 
insure  this,  the  resistance  of  the  filament  must  necessarily 
l)e  uniform  .per  unit  of  length,  since,  otherwise,  on  the 
passage  of  a  steady  current  through  it,  different  parts 
would  glow  with  unequal  brightness  and  the  parts  un- 
duly heated  would  be  rapidly  destroyed,  or,  if  preserved 
at  the  safe  temperature,  the  rest  of  the  filament  would  be 
insufficiently  heated. 

214-.  The  standard  of  physiological  effective  luminous 
radiation,  or,  as  it  is  ordinarily  called,  the  standard 
of  light,  differs  in  different  countries.  In  the  United 
States  and  in  Great  Britain  it  is  the  standard  candle 
burning  2  grains  (0.1296  gramme)  per  minute ;  in  France, 
a  Carcel  lamp  of  definite  dimensions,  burning  42  grammes 
of  colza  oil  per  hour ;  in  Germany,  a  Hefner- AltenecJc 
lamp  of  definite  dimensions  burning  amyl-acetate  with  a 
flame  four  cms.  high.  The  light  emitted  from  one  square 
centimetre  of  platinum  at  a  definite  high  temperature  is 
also  employed  as  a  standard  in  Germany  under  the  name 
of  the  Reichsanstalt  Unit.  In  France  the  Violle  lamp 
of  molten  platinum  was  adopted  by  the  International 
Paris  Conference  of  1881,  but  has  not  come  into  general 
use. 

According   to   the   best   determinations   one   standard 


206 


British  candle  =  0.0506  Violle,  =  0.1053  carcel,  =  1.14 
Hefner  Alteneck. 

215.  The  illumination  received  by  any  surface  is  the 
quantity  of  light  (the  physiologically  effective  flux 

of  light)  received  by  its  surface  per  unit  area.  Thus,  if 
the  standard  candle  be  regarded  as  the  unit  point-source 
of  light,  the  total  quantity  of  light  it  emits  is  4  TT,  units 
of  luminous  flux,  and  one  unit  of  luminous  flux  received 
per  square  centimetre  would  constitute  unit  illumination. 
No  name  or  unit  of  illumination  has,  however,  yet  been 
adopted,  but  common  expressions  of  illumination  refer  to 
the  candle-foot,  or  the  carcel-metre  as  unit,  these  being 
respectively  the  illumination  produced,  on  a  perpendicu- 
lar surface  by  a  candle  at  a  distance  of  one  foot,  and  by 
a  carcel  at  a  distance  of  one  metre.  These  intensities 
of  illumination  are  nearly  equal,  one  candle-foot  being 
greater  than  one  carcel-metre  in  the  approximate  ratio  of 
1.133. 

216.  The  proper  lighting  of  a  room  depends  upon  its 
dimensions,  and  upon  the  character  of  its  interior 

surface.  Highly  diffusive  wall  surfaces  require  a  smaller 
amount  of  light  to  produce  the  same  general  degree  of 
illumination.  The  character  of  the  illumination  will 
also  depend  upon  the  amount  of  light  and  upon  its  dis- 
tribution. A  single  source  of  light  will  usually  produce 
the  greatest  local  and  the  lowest  average  illumination, 
while  the  same  total  quantity  of  light  from  numerous 
distributed  sources  will  produce  the  opposite  results.  In 
the  case  of  incandescent  lamps,  an  illumination  upon  the 
surface  of  a  book,  equivalent  to  one  carcel-metre,  is  suf- 
ficient for  the  purposes  of  easy  reading.  This  is  usually 
obtained  in  a  room  by  allowing  1  candle  power  to  the 


207 


square  foot  of  floor  space,  or  one  16  c.  P.  lamp  to  50  sq. 
feet,  while  rooms  not  devoted  to  reading  purposes,  unless 
darkly  papered,  will  be  amply  illumined  by  one  16  c.  P. 
lamp  per  100  sq.  feet  of  floor  space.  The  intensity  of 
illumination  from  a  single  point-source  of  light  is  inversely 
as  the  square  of  the  distance  from  tlie^  source,  so  that  a 
room  with  a  high  ceiling,  lighted  by  incandescent  lamps 
placed  on  the  ceiling,  would  receive  on  a  desk  or  table  a 
lesser  degree  of  illumination  than  if  the  lamp  were  lower, 
and,  in  any  case,  the  illumination  on  the  surface  of  the 
desk  or  table  is  ordinarily  greater  than  on  the  surface  of 
the  floor.  In  determining,  therefore,  the  number  of  in- 
candescent lamps  required  for  the  proper  illumination  of 
a  room,  reference  must  be  had  not  only  to  the  character 
of  the  illumination  but  to  the  parts  of  the  room  where 
such  illumination  is  specially  required. 

217.  The  number  of  watts  that  have  to  be  supplied  to 
an  incandescent  lamp  per  candle  power  that  it 

yields  is  frequently  called  the  efficiency  of  the  lamp,  but 
could  more  accurately  be  called  the  inefficiency  of  the 
lamp  or  its  specific  activity r,  since  the  greater  the  number 
of  watts  supplied  per  candle  obtained,  the  lower  the  ef- 
fective physiological  efficiency  of  the  lamp. 

The  true  efficiency  of  the  lamp,  or  its  specific  illumi- 
nating power,  is  the  reciprocal  of  this,  or  the  number  of 
candles  obtained  from  the  lamp  per  watt  supplied  to  it. 
The  efficiency  at  which  new  lamps  are  usually  operated, 
ranges  between  -i-  and  ^  candles  per  watt. 

218.  The  higher  the  temperature  at  which  a  lamp  is 
operated  the  greater  its  efficiency,  but  the  shorter 

its  probable  duration  of  life. 


208 


When  an  incandescent  lamp  is  steadily  operated  at 
constant  pressure,  the  light  it  emits  steadily  decreases, 
that  is,  its  efficiency  becomes  reduced.  This  is  owing  to 
two  causes  consequent  upon  the  disintegration  of  the  fil- 
ament. First,  to  the  deposition  of  the  disintegrated 
material  as  an  opaque  coating  on  the  walls  of  the  lamp 
globe,  thereby  reducing  the  amount  of  light  emitted,  and 
second,  to  the  reduction  in  the  cross-section  of  the  tila- 
ment  by  the  disintegration  and  the  consequent  increase 
in  resistance,  whereby  less  energy  is  absorbed  by  the 
lamp.  .-  » 

SYLLABUS. 

The  physiological  effect  on  the  retina  of  different  re- 
lative frequencies  within  visible  limits  is  different ;  gener- 
ally, therefore,  the  physiological  effect  of  a  given  quantity 
of  luminous  activity  varies  with  different  sources  of  light. 

The  illumination  required  on  a  well  lighted  table  in 
an  ordinary  room  is  about  one  carcel-rnetre,  or  usually, 
two  sixteen  candle  power  lamps  for  every  100  square 
feet  of  floor  space. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 
WEEKLY. 

No.  27.  DECEMBER  15,  1894. 

Electrical   Engineering   Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED     GRADE. 

INCANDESCENT     LIGHTINQ 


219.  When  a  new  incandescent  lamp  is  connected 
to  mains  which  supply  it  uniformly  with  the 
pressure  for  which  it  was  designed,  say,  for  example,  a 
pressure  of  110  volts,  the  lamp  having  an  initial  resist- 
ance when  hot  of  252  ohms,  the  current  through  the 
lamp  will  be  0.4364  ampere,  and  the  activity  in  the 
lamp  will  be  48  watts ;  or,  if  the  lamp  supplies  16  c.  P., 
an  efficiency  of  |  candle  per  watt.  The  first  effect  of 
the  high  temperature  upon  the  filament,  may  be  to  re- 
duce its  resistance  by  a  coking  or  carbonizing  process 
sustained  by  heating  in  a  vacuum.  The  current, 
therefore,  which  passes  through  the  lamp,  together  with 
the  activity  of  the  lamp,  will  increase  in  corresponding 
measure,  thereby  increasing  the  temperature  of  the 
filament,  and  the  candle-power  as  well  as  the  efficiency 
of  the  lamp.  Tiiis  diminution  in  resistance,  which, 
however,  does  not  occur  in  all  lamps,  soon  ceases,  and, 
after  say  twenty  hours,  the  resistance  of  the  filament 
begins  to  increase. 

Published  by 
THE   ELECTRICAL   ENGINEER, 

203  Broadway,  New  York,  N.  Y, 

[.Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  June  14,  189}.] 


210 


The  candle-power  of  the  lamp  attains  its  maximum 
with  the  minimum  resistance  of  the  filament. 

220.  The  temperature  of  the  filament  in  incandes- 
cent lamps,  operated  at  an  efficiency  of  J  candle 

per  watt,  is  estimated  to  be  about  1345°  C.;  at  |  candle 
per  watt  about  1310°  C.;  and  at  ¥*T  candle  per  watt 
about  1290°  C.  An  increase  of  one  per  cent,  in  the 
activity  of  a  glowing  lamp,  i.e.,  in  the  number  of  watts 
it  absorbs,  is  believed  to  increase  the  temperature  of  its 
filament  about  2°  C.  and  its  candle-power  or  its  total 
flux  of  light  about  three  per  cent. 

221.  The  progressive  increase  in  the  resistance  of  the 
filament  during  use,  is  due  to  the  reduction  in  the 

diameter  and  cross-sectional  area  of  the  filament.  This 
reduction  in  the  diameter  of  the  filament  is  brought  about 
*by  one  or  all  of  the  following  causes  ;  namely, 

(^.)  Mechanical,  by  the  explosive  evolution  of  occluded 
gases  in  the  surface  layers  of  the  filament. 

(2.)  Chemical,  by  the  removal  of  the  surface  layers 
of  the  filament  through  chemical  combination  with  some 
of  the  constituents  of  the  residual  gases  in  the  globe. 

(3.)  Physical,  by  electrical  evaporation  of  the  surface 
layers  under  the  influence  of  high  temperature  and  elec- 
trification. 

222.  Not  only  is  the  diameter  of  the  filament  de- 
creased and  its  resistance  thereby  increased,  but 

the  emissivity  of  the  surface  is  considerably  increased. 

The  temperature  of  the  filament  is  thus  lowered  dur- 
ing the  use  of  the  lamp  for  two  reasons  ;  first,  because 
the  emissivity  of  the  surface  increases  by  reason  of  the 
surface  change,  thus  enabling  the  same  quantity  of  activ- 


ity  per  unit  surface  to  be  radiated  at  a  lower  tempera- 
ture, and  secondly,  because  the  diminished  conductance 
of  the  filament  causes  it  to  take  less  activity  from  the 
mains  in  the  same  proportion.  There  is  thus  less  activ- 
ity in  the  lamp  and  also  less  temperature  elevation  re- 
quired to  radiate  the  activity  that  remains. 

223.  The  carbon  which  is  thus  removed  from  the 
surface  of  the  filament  is  slowly  deposited  on  the 

inside  of  the  lamp  globe  in  a  dark  semi-opaque  layer, 
cutting  off  some  of  the  light  emitted  by  the  filament 
and,  therefore,  tending  to  reduce  the  efficiency  of  the 
lamp.  Each  of  these  three  causes ;  namely,  increased 
resistance,  increased  emissivity,  and  increased  opacity, 
decreases  the  efficiency  of  the  lamp  to  approximately 
the  same  degree.  As  a  consequence,  new  lamps  starting 
at  an  efficiency  of  ^  candle  per  watt,  steadily  decrease 
in  their  efficiency  after  the  first  few  hours,  until  an 
efficiency  even  lower  than  ^  candle  per  watt  may  be  ulti- 
mately reached. 

224.  The  physiologically  effective  luminous  radiation 
from  a  lamp  increases  rapidly  with  the  current, 

between  the  fifth  and  sixth  powers  of  the  current  strength. 
Since  at  incandescent  temperatures,  the  temperature 
coefficient  of  variation  in  the  resistivity  of  the  filament 
is  small,  and  a  small  change  of  temperature  is  accom- 
panied by  a  great  change  in  candle  power,  it  follows  that 
the  candle-power  of  a  lamp  varies  with  the  terminal 
voltage  between  its  fifth  and  sixth  powers,  and  therefore 
approximately  as  the  cube  of  the  intake  in.  watts. 

Since  the  efficiency  of  a  lamp  steadily  decreases  with 
its  continued  use,  there  must  come  a  time  when  even  if 


212 


the  filament  does  not  break,  the  light  emitted  becomes 
so  small  in  proportion  to  the  power  consumed,  that  it 
may  be  more  economical  to  destroy  the  lamp  and  replace 
it  by  a  new  one,  than  to  continue  its  use  at  such  low 
efficiency.  The  length  of  time  during  which  it  will 
be  advantageous  to  continue  the  use  of  such  a  lamp  will 
depend  on  the  cost  of  electrical  energy  and  on  the  cost 
of  new  lamps.  Although  this  may  be  determined  on  a 
large  scale  of  operation,  as  in  central  station  lighting,  it 
is  practically  impossible  to  lay  down  an  inflexible  rule 
for  the  economical  breaking  point  of  any  lamp,  since  it 
is  evidently  economical  to  retain  a  lamp  in  employment 
so  long  as  it  supplies  sufficient  light  to  meet  the  purposes 
required  of  it. 

225.  In  large  cities  in  the  United  States,  practical 
experience  in  central  station  work  shows  that  the 

maximum  load  is  approximately  50  per  cent,  of  the  total 
number  of  lamps  connected  with  the  system,  that  the 
average  load  is  approximately  27  per  cent,  of  the  maxi- 
mum load  and  the  minimum  load  from  10  to  20  per  cent, 
of  the  maximum  load. 

226.  Attempts  have  been  made  at  different  times  to 
produce  a  lamp  capable  of   being  regulated   in 

candle  power,  when  supplied  from  constant  potential 
mains,  thus  corresponding  to  the  gradual  turning  off  at 
the  key  in  a  gas  burner.  This  has  been  accomplished  in 
the  case  of  the  incandescent  lamp  in  two  ways;  first,  by 
introducing  additional  resistance  into  the  lamp  circuit 
and,  second,  by  reducing  the  time  during  which,  in 
periodic  contacts,  the  iilament  is  in  connection  with  the 
mains.  Both  methods  result  in  a  considerable  reduction 


213 


of  efficiency  in  the  lamp,  and  a  diminished  temperature 
of  the  filament,  so  that  the  light  is  not  only  more  expen- 
sively produced  but  also  becomes  duller  in  color. 

227.  In  large  installations  where  the  number  of  lights 
required  is  great  and  the  distance  from  the  supply 

centre  not  excessive,  incandescent  lamps  are  almost  in- 
variably connected  to  the  supply  mains  in  parallel.  The 
parallel  connection  method  of  distribution  is  both  simple 
and  economical.  But  where  the  district  to  be  lighted  is 
scattered,  necessitating  long  circuits  on  which  the  density 
of  lighting  is  not  great,  this  method  becomes  very  ex- 
pensive in  all  cases  where  a  comparatively  small  drop  is 
to  be  maintained  on  the  supply  mains.  In  such  cases  it 
is  more  economical  to  employ  a  high  tension  system ; 
that  is,  either  a  series-connected  system ;  or,  as  is  more 
common,  an  alternating  current  system  in  connection 
with  transformers.  In  a  series  incandescent  system,  the 
lamps  are  connected  to  the  circuit  in  series.  The  resist- 
ance of  series  incandescent  lamps  is  usually  compara- 
tively small  and  the  current  they  take  greater  than  in 
multiple  incandescent  lamps.  In  many  cases  incandes- 
cent lamps  are  connected  in  series  arc  circuits,  and,  there- 
fore, require  to  be  operated  by  the  current  generally 
employed  in  such  circuits,  namely,  about  10  amperes. 

228.  The  rupture  of  a   filament,  which  merely  ex- 
tinguishes the  lamp  in  a  multiple-connected  cir- 
cuit, in  a  series  circuit  extinguishes  all  the  lamps  in  that 
circuit,  unless  a  device  be  employed  to  cut  out  the  im- 
perfect lamp.    This  is  frequently  accomplished  by  means 
of  a  film  cut-out.     Fig.  73  shows  a  series  incandescent 
lamp  and  a  film  cut-out  arranged  in  the  lamp  base.    This 


cut-out  consists  of  a  film  of  paper  which  insulates  per- 
fectly at  a  pressure  of  20  volts,  but  breaks  down  com- 
pletely under  a  pressure  approaching  that  of  the  full 
pressure  in  the  circuit,  so  that  the  two  contact  points 
separated  by  the  film  become  welded  together  as  soon 
as  the  lamp  breaks.  This  cut  out  is  placed  either  in  the 
base  of  the  lamp  or  in  the  socket. 

529.     Since  one  per  cent,  change  in  the  pressure  sup- 
plied to  the  terminals  of  an  incandescent  lamp, 
above  or  below  the  normal  pressure,  produces  about  5 


FIG  73. 

Series  Incandescent  Lamp  with  Film  Cut-Out. 

per  cent,  change  in  the  amount  of  light  supplied  by  the 
lamp,  it  is  necessary  to  ensure  that  the  drop  of  pressure 
in  the  mains  supplying  different  lamps  shall  not  be  ex- 
cessive. Where  a  large  number  of  lamps  have  to  be 
supplied  in  parallel  from  a  network  of  mains,  the  pres- 
sure will  be  lowest  at  the  most  distant  lamps.  If  when 
all  the  lamps  are  lighted,  the  maximum  drop  of  the 
most  distant  lamps  amounts  to,  say,  10  per  cent,  of  the 
pressure  of  the  dynamos,  then  it  is  desirable  to  make 
the  average  pressure  for  the  whola  system,  the  normal 


215 


pressure  for  which  the  lamps  are  designed.  In  this  case 
the  distant  lamps  will  be  operated  at  5  per  cent,  below 
pressure,  while  those  nearest  to  the  dynamo  will  be  oper- 
ated at  5  per  cent,  above  pressure.  This  will  -reduce 
the  average  life  of  the  nearest  lamps  in  a  very  marked 
degree,  while  the  distant  lamps,  will  be  below  candle- 
power  by  an  amount  which  depends  upon  their  normal 
efficiency.  The  usual  range  of  drop  permitted  in  the 
wiring  of  buildings  supplied  by  their  own  dynamos  is 
from  2  to  5  per  cent,  of  the  pressure  at  the  dynamo  ter- 
minals, according  to  the  size  of  the  building,  i.e.,  from 
1  to  2^  per  cent,  above  or  below  the  normal  mean.  So 
that,  allowing  5  per  cent,  drop,  if  the  normal  voltage  of 
the  lamps  be  110,  the  dynamo  pressure  would  be  112.8 
and  the  pressure  at  the  lowest  lamp  107.2  volts.  The 
lamps  nearest  the  dynamos  would,  therefore,  give  say  19 
candles  initially  and  the  lamps  furthest  from  the  dynamo 
13.5  candles. 

230.  The  difficulty  arising  from  drop  experienced  in 
the  lightiLg  of  a  single  building,  is  greatly  in- 
creased when  the  lighting  has  to  be  extended  over  a 
large  area,  in  a  city,  from  a  single  central  station.  In 
such  cases  excessive  drop  may  be  avoided  by  the  use  of 
suitably  located  and  proportional  feeders.  A  feeder  is  a 
conductor,  one  end  of  which  is  connected  to  the  bus- 
bars at  the  station,  and  the  other  end  is  connected  to 
some  point  on  the  mains,  there  being  no  lamps  connected 
directly  to  the  feeders,  so  that  the  mains  supply  the 
lamps,  while  the  feeders  supply  the  mains.  In  this  way 
it  is  possible  to  maintain  say  110  volts  at  a  very  distant 
lamp,  with  a  drop  of  perhaps  three  volts  in  the  mains, 
making  113  volts  at  the  feeding  point,  but  with  a  drop 


or 


216 


of  17  volts  in  the  feeder  or  feeders,  and  a  pressure  of 
130  volts  at  the  central  station.  In  other  words,  it  is 
possible  to  have  15  or  20  per  cent,  drop  in  the  feeders 
and  only  a  very  small  range  of  drop  in  the  mains  and 
house  wires. 

The  number  and  size  of  feeders  employed  in  distrib- 
uting currents  from  a  central  station  depends  upon  the 
cost  of  the  power  which  has  to  be  expended  in  the  drop 
under  existing  conditions  of  load,  upon  the  cost  of  the 
various  sizes  of  feeder,  upon  the  facility  with  which  the 
pressure  can  be  maintained  uniform  at  feeder  terminals 
and  its  effect  upon  the  average 'life  time  and  proper 
operation  of  lamps.  Feeders  have  to  be  so  selected  that 
the  total  cost,  including  these  items,  together  with  depre- 
ciation shall  be  a  minimum. 

SYLLABUS. 

The  resistance  of  an  incandescent  lamp  increases  with 
its  use. 

This  increase  is  due  to  a  decrease  in  its  diameter  that 
may  be  produced  by  mechanical,  chemical  and  physical 
causes. 

The  effect  of  the  decrease  of  the  diameter  of  the  fila- 
ment is  not  only  accompanied  by  an  increase  in  its  re- 
sistance, but  also  by  an  increase  in  the  emissivity  of  its 
filament  and  by  a  blackening  of  the  globe. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 
WEEKLY. 

NY>    9S  "n-uwc'Ttni-E'i?  99    1 SQJ.         Price,    -    10  Cents. 

,EMBEK  JJ,  1    *k.        Subscnption,  $3.00. 

Electrical   Engineering   Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED      CF?AE>E 

ARC    LlQHTINQ. 


23 1 .  The  voltaic  carbon  arc  consists  of  a  bow-shaped 
cloud  of  volatilized  carbon,  formed  between  the 
points  of  two  carbon  electrodes  by  the  passage  of  an 
electric  current.  In  order  to  produce  this  current,  a 
pressure  of  from  30  to  55  volts  has  to  be  maintained 
between  the  carbon  electrodes.  This  pressure  is 
required  by  reason  of  resistances  in  the  arc,  and  partly 
by  a  c.  E.  M.  F.  The  c.  E.  M.  F.  depends  upon  the  quality 
of  the  carbons  employed  and  the  temperature  attained. 
When  the  arc  is  very  short,  the  temperature  is  compara- 
tively low,  and  the  c.  E.  M.  F.  comparatively  small,  but 
for  arcs  of  -J  in.  or  more,  the  c.  E.  M.  F.  varies  from  35  to 
40  volts,  and  the  drop  due  to  resistances  increases  with 
the  length  of  arc,  being  about  50  to  75  volts  per  inch, 
(20  to  30  volt  per  cm.),  of  distance  between  the  elec- 
trodes. The  current  strength  employed  varies  from  3 
to  200  amperes,  according  to  the  size  and  nature  of  the 
carbons.  Consequently,  the  activity  in  the  carbon  voltaic 

Published  by 

THE  ELECTRICAL  ENGINEER, 
•03  Broadway,  New  York,  N.  Y. 

[Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  June  14,  1804.] 


218 


arc  may  have  a  very  wide  range.  The  ordinary  com- 
mercial arc  lamp  takes  about  10  amperes  at  45  volts 
pressure  between  lamp  terminals,  and,  therefore,  has  an 
activity  of  about  450  watts.  Such  an  arc  lamp  is  some- 
times described  as  a  450-watt  arc  lamp,  but  is  more  pre- 
cisely described  as  a  450-watt  45-volt  arc  lamp. 

232.  Of  the  E.  M.  F.  in  the  arc   lamp,  about  38  to 
40  volts  are  usually  developed  at  the  surface  of  the 

positive  electrode,  4  to  6  volts  in  the  arc  proper,  and  the 
remainder  in  the  carbon  rods  and  the  electromagnetic 
apparatus.  The  activity  is,  therefore,  about  400  watts 
at  the  surface  of  the  positive  carbon,  40  to  60  watts  in 
the  arc  proper,  and  the  remainder  in  the  substance  of 
the  carbons  and  conductors.  So  large  a  proportion  of  the 
activity  at  the  positive  carbon  surface,  necessitates  the 
development  there  of  an  exceedingly  high  temperature, 
and,  consequently,  this  is  the  principal  source  of  light  in 
the  voltaic  arc,  about  85  per  cent,  of  all  the  light  being 
emitted  from  the  glowing  surface  of  the  positive  carbon, 
about  10  per  cent,  from  the  arc  proper,  and  about  five 
per  cent,  from  the  surface  of  the  negative  carbon. 

233.  The  high  value  of  the  c.  E.  M.  F.,  developed  at  the 
positive  surface,  is  analagous  to  the  c.  E.  M.  F.  de- 
veloped at  the  surface  of  the  electrode  in  an  electrolytic 
cell.     In  this  case,  however,  the  work  is  not  expended 
in  freeing  ions  from  molecular  combinations,  but  in  vola- 
tilizing carbon,  and  the  high  temperature  is  accompanied 
by  intense  radiation.     Consequently,  all  the  volatilization 
occurs  at  the  end  of  the  positive  carbon,  which  is  thereby 
hollowed  out  in  the  form  of  a  minute  crater,  the  principal 
source  of  light  in  the  arc.     The  character  of  the  lumin- 


ous  radiation  will  depend  on  the  quality  of  the  carbon 
electrodes  and  their  distance  apart ;  but,  with  the  same 
material,  the  distance  being  maintained  constant,  the 
temperature  at  the  surface  of  the  positive  carbon  will  be 
uniform  if  the  current  strength  is  adequately  main- 
tained.- Carbon  having,  like  other  substances  under 
fixed  conditions,  a  fixed  temperature  of  volatilization, 
(estimated  at  3,500°  C.),  the  temperature  at  the  posi- 
tive carbon,  and  consequently  the  intensity  of  radiation, 
are  thereby  determined.  It  has  been  found  that  the 
brightness  of  the  positive  crater  amounts  to  about  16,000 
British  standard  candles  per  square  centimetre,  or, 
roughly,  100,000  candles  per  square  inch. 

The  negative  carbon  is  at  a  temperature  sufficiently 
below  that  of  the  positive  to  permit  the  volatilized  car- 
bon to  be  condensed  upon  its  surface  in  the  shape  of  a 
small  mound  or  nipple  of  graphite. 

234.  The  temperature  of    volatilization    of    carbon 
being  so  much  greater  than  that  at  which  carbon 

monoxide  forms,  is  probably  above  the  dissociation  tem- 
perature of  carbon  and  oxygen,  so  that  the  carbon  vapor 
can  only  oxydize  at  the  external  surface  when  the  tem- 
perature suddenly  falls.  This  accounts  for  the  coating 
of  flame  which  surrounds  the  arc  itself,  and  for  the  com- 
paratively slow  rate  of  carbon  consumption. 

235.  With  the  carbons  arranged  as  is  usual  in  street 
lamps  with   both   carbons   in   the  same  vertical 

line  the  positive  above  the  negative,  the  amount  of 
light  given  off  from  the  arc  varies  in  different  angular 
positions.  This  difference  in  the  intensity  of  the  emitted 
light  is  due  to  the  following  circumstances : 


220 


(1.)  The  positive  crater,  the  main  source  of  light,  is  not 
a  plane  surface,  but  is  concave  ;  the  principal  distribution 
of  its  radiant  flux  is,  consequently,  downwards. 

(2.)  The  crater  being  surrounded  by  a  wall  of  opaque 
carbon,  the  horizontal  intensity  of  the  emitted  light  is 
comparatively  small,  and,  since  the  edges  of  the  wall  are 
irregular,  the  horizontal  intensity  varies  in  different 
azimuths. 

(3.)  However  closely  the  axis  of  the  two  carbon  elec- 
trodes may  be  aligned,  the  arc  will  rarely  remain  long  at 


Elec.  Engineer 

FIG.  74. 

Diagram  Indicating  Luminous  Intensity  of  an  Arc  Lamp  in  Different  Directions. 

the  centre,  but  tends  to  travel  around  the  edges  of  the 
positive  carbons,  thereby  causing  the  crater  to  appear  on 
the  side  of  the  arc,  and  tending  to  increase  the  illumina- 
tion on  that  side. 

(4.)  The  arc  is  usually  accompanied  by  some  flame  of 
a  reddish  color  surrounding  the  arc  proper,  like  a  lum- 
inous cloud,  and  the  light  from  this  source  is  of  an 
unstable  flickering  nature,  shifting  irregularly. 

5.  Even  the  smallest  mechanical  irregularity  or  chemi- 
cal impurities,  liable  to  be  present  in  the  best  carbons, 
develop  fluctuations  in  the  intensity  of  the  light. 


221 


Fig.  74  represents  graphically,  in  polar  co-ordinates,  the 
relative  distribution  of  luminous  intensity  from  an  ordi- 
nary 500-watt,  50- volt  arc  lamp.  It  will  be  seen  that  the 
maximum  intensity  is  developed  at  an  angle  which  is  ap- 
proximately 50°  below  the  horizontal  plane.  The  hori- 
zontal intensity  is  usually  only  about  10  to  20  per  cent, 
of  the  maximum  intensity,  and,  in  the  actual  example 
here  represented,  o  B,  or  o  G  is  only  about  11  per  cent,  of 
o  c,  or  o  F.  The  horizontal  intensity  is  subject,  owing  to 
the  causes  above  mentioned,  to  much  greater  fluctuations 
than  the  maximum  intensity.  The  mean  spherical  can- 
dle power  is  the  average  intensity  measured  in  candle- 
power  for  all  directions.  The  mean  spherical  candle- 
power  is  usually  about  30  to  40  per  cent,  of  the  maxi- 
mum intensity  and  from  2  to  4  times  greater  than  the 
horizontal  intensity.  In  Fig.  74  the  radius  o  j  is,  in 
length,  30  per  cent,  of  the  radius  o  c,  or  o  F.  The  ordi- 
nary empirical  formula  which  fairly  expresses  the  ob- 
served relationship  between  the  spherical  and  maximum 
intensities  is, 
Mean  spherical  intensity  = 

Mean  horizontal  intensity     ,     Maximum  intensity. 

HP  ~T~ 

It  is  evident  that  the  total  quantity  of  light  emitted 
will  be  4  TT  X  mean  spherical  intensity  in  units  of  lu- 
minous flux. 

236.  The  nominal  intensity  of  an  arc  lamp,  as  for  ex- 
ample, that  of  a  2,000  candle-power  arc,  means  the 
maximum  intensity  of  the  arc  under  favorable  conditions 
of  carbons  and  operation.  A  preferable  rating,  however, 
would  be  either  by  the  total  luminous  flux  of  the  arc 
lamp  or  its  mean  spherical  candle-power. 


The  greater  the  current  strength  through  an  arc  lamp 
the  greater  the  surface  which  becomes  elevated  in  tem- 
perature. If  the  carbons  are  too  small,  this  will  be  ac- 
accompanied  by  flaming  disintegration,  and  other  dis- 
turbances, but  if  the  carbons  be  suitably  increased  in 
diameter,  the  increase  in  total  luminous  flux  will  be 
safely  obtained.  For  a  given  arc  lamp  of  48  volts  pres- 
sure, it  has  been  observed  that  an  empirical  relation  exists 
between  the  intensity  of  the  current  strength  fairly  ex- 
pressed by  the  formula, 

Maximum  luminous  intensity  =  190  i  -f-  4  iz, 
where  *  =  current  strength  in  amperes. 

So  that  a  480-watt,  10-ampere  arc  lamp  gives  under 
favorable  conditions  a  maximum  intensity  of  2,300 
candles. 

237.  A  great  difficulty  exists  in  accurately  measuring 
the  candle  power  of  an  arc-lamp  by  the  use  of 
any  of  the  ordinary  standards  of  light.  This  difficulty 
is  due  not  only  to  the  rapid  fluctuations  constantly  occur- 
in  the  arc,  but  also  to  the  difference  in  the  character  be- 
tween the  light  of  the  arc  and  that  of  the  ordinary 
standards  with  which  it  is  compared.  An  arc  lamp  is 
particularly  rich  in  waves  of  high  frequency  ;  namely, 
those  near  the  violet  end  of  the  spectrum,  and  the  eye  is 
unable  fairly  to  match  intensities  between  lights  of  es- 
sentially different  colors.  This  difficulty  has  led  to  the 
proposal  of  a  special  standard  for  arc  lamp  photometry, 
based  on  the  relation  which  has  been  found  to  exist  be- 
tween the  amount  of  light  emitted  per  unit  surface  of  the 
crater  in  the  positive  carbon. 

The  arc  lamp  whose  luminous  intensity  is  to  be  meas- 
ured is  compared  in  the  photometer  with  what  might  be 


223 


called  a  unit-arc-light  crater-intensity,  which  consists 
of  a  standard  arc  lamp  whose  crater  is  exposed  to  the 
photometer  through  an  opening  of  standard  dimensions 
in  an  opaque  and  artificially  cooled  screen. 

Most  arc  light  carbons,  in  use  in  the  United  States, 
are  provided  with  a  thin  metallic  coating  of  copper, 
electrolytically  deposited.  The  effect  of  this  coat- 
ing is  not  only  to  decrease  the  resistance  of  the  rods, 
but  also  to  prevent  irregular  burning  and  disintegration. 
Carbons  so  protected  are  more  apt  to  burn  with  com- 
paratively blunt  ends,  and,  therefore,  to  last  longer. 
Unprotected  carbons  are  apt  to  burn  in  points,  and  thus 
seriously  interfere  with  the  proper  feeding  of  the 
carbons,  that  is,  their  automatic  adjustment  as  to  distance. 

238.  During  use,  the  carbons  consume  unequally. 
The  positive  carbon  consuming  roughly  twice  as 
rapidly  as  the  negative  carbon.  The  more  rapid  con- 
sumption of  the  positive  carbon  is  due  not  only  to  the 
higher  temperature  but  also  to  the  fact  that  it  is  volatil- 
ized. For  this  reason  the  positive  carbon  is  generally 
made  about  twice  as  long  as  the  negative  carbon. 
Attempts  have  been  made  to  prolong  the  duration  of 
the  carbons  by  increasing  their  diameter,  but  whenever 
the  diameter  of  the  carbon  exceeds  a  certain  limit,  de- 
pending upon  the  strength  of  the  current,  the  light  be- 
comes unsteady,  owing  to  the  tendency  of  the  arc  to 
travel  around  the  edges  of  the  larger  cross  section 
offered.  Less  objection  is  experienced  to  increasing  the 
diameter  of  the  negative  carbon,  alone,  but  even  here, 
the  increased  duration  is  accompanied  by  increased  fluc- 
tuations in  the  light. 

The  average  length  of  the  positive  carbons  employed 


224 


in  systems  of  street  lighting  does  not  usually  exceed  12 
inches,  the  length  of  the  negative  carbon  being  about 
seven  inches.  Such  a  pair  of  carbons  will  ordinarily 
last  about  7  hours  when  T\-  in.  in  diameter,  and 
about  9  hours  when  £  in.  in  diameter.  Consequently, 
during  prolonged  runs,  such  as  are  necessitated  during 
winter,  a  lamp  provided  with  but  a  single  pair  of  such 
carbons  would  require  re-carboning  during  the  night.  In 
order  to  avoid  this,  various  expedients  have  been  adopted, 
such  as  an  increase  in  the  diameter  of  carbons  already 
alluded  to.  The  method  in  general  use  is  that  of  employ- 
ing two  pairs  of  carbons  side  by  side,  so  arranged  that  one 
pair  of  carbons  is  first  consumed  and  the  second  pair  is 
then  automatically  switched  into  the  circuit.  Such  a  lamp 
is  commonly  called  a  dou~ble-carbcm,,  or  all-night  lamp. 

SYLLABBUS. 

The  c.  E.  M.  F.  of  a  carbon  voltaic  arc  is  principally 
resident  at  the  surface  of  the  carbon  electrode  or  crater. 

It  is  commonly  considered  that  a  450-watt  45-volt  arc- 
lamp  gives  a  maximum  of  2,000  candle-power,  but  this 
is  only  true  under  the  most  favorable  conditions. 

An  arc  light  differs  principally  from  the  light  of 
candles,  incandescent  lamps  and  other  luminous  sources, 
in  being  richly  provided  with  luminous  waves  of  high 
frequency. 

The  mean  horizontal  intensity  of  an  arc  lamp  is  much 
more  variable  than  its  maximum  intensity,  but  is  com- 
monly about  15  per  cent,  of  the  maximum  intensity. 

The  mean  spherical  intensity  of  an  arc  lamp  is  about 
35  per  cent,  of  its  maximum  intensity. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 
WEEKLY. 


No.  29.  DECEMBER  29,  1894. 

Electrical   Engineering  Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED      CF?ADE 

ARC  LIOHTINO. 


239.  On  constant  current  circuits,  arc  lamps  are 
generally  operated  in  series  and  are  then  supplied 
by  special  generators  known  as  arc-light  dynamos. 
These  generators  are  always  series-wound.  The  number 
of  lamps  operated  in  series  is  commonly  about  50, 
though  occasionally  it  reaches  about  100,  and  in  rare  in- 
stances 200.  The  largest  arc  generator  yet  constructed 
being  for  200  lamps,  a  pressure  of  about  10,000  volts  exists 
between  machine  terminals.  Since  the  number  of  arc 
lights  in  a  circuit  is  seldom  constant,  the  generator 
must  maintain  a  constant  current  under  all  conditions 
and  must  be  able  to  vary  the  E.  M.  F.  it  generates. 

When  a  series  arc-light  circuit,  Fig.  750,  containing  say 
10  lamps,  and  having  a  total  pressure  at  machine  termin- 
als of  500  volts,  is  perfectly  insulated  from  the  ground, 
there  will,  by  symmetry,  be  a  difference  of  potential  be- 
tween the  positive  brush  and  the  ground  of  250  volts, 
and  a  difference  of  potential  between  the  negative  brush 

Published  by 

THE   ELECTRICAL  ENGINE 
203  Broadway,  New  York,  N. 

[Entered  as  second-class  matter  at  the  New  York,  N.  YM 


226 


and  the  ground  of  an  equal  amount,  while  a  point  B,  in  the 
circuit,  situated  electrically  midway  between  the  termi- 
nals, will  be  at  zero  potential,  and  could,  therefore,  be  con- 
nected to  the  ground  without  in  any  way  disturbing  the 
pressures  or  current  strengths  in  the  circuit.  If,  however, 
instead  of  connecting  the  circuit  to  ground  at  its  central 
point,  the  ground  connection  were  made  at  any  other 
point,  such,  for  example,  as  at  the  positive  terminal  of 
the  generator,  D,  Fig.  75&,  that  point  would  be  reduced 


1-200 

O.-HOO 


—I 


o 

-100 
-200? 
--300Q 
-400  > 
-500 


-t-400 
«  H-  300' 
^+200 
>+lOO 


Elec.Engineer 

FIG.  75. 

Distribution  of  Electric  Potential  in  Continuous  Current  Series  Arc  Circuit. 

to  zero  potential,  the  symmetry  of  pressure  at  the 
dynamo  terminals  would  be  disturbed  and  the  potential 
of  the  negative  terminal  would  become  500  volts.  Sim- 
ilarly, if  the  ground  connection,  instead  of  being  made 
at  D,  were  made  at  G,  Fig.  75tf,  the  potential  at  that  point 
would  be  reduced  to  zero,  producing  the  distribution 
of  potential  shown.  There  would,  however,  be  no 
permanent  flow  of  current  from  the  circuit  through  the 
ground  connection  while  the  insulation  of  the  rest  of  the 


227 


circuit  is  preserved.  If,  however,  a  second  ground  con- 
nection occur,  then  a  current  would  flow  through  both 
ground  connections  of  a  strength  determined  by  the 
resistance  of  the  ground  connections  and  the  difference 
of  potential  between  the  points  of  contact. 

Thus  if,  Fig.  75c,  a  slight  leak  to  ground  were  at- 
tached at  the  point  H,  the  E.  M.  F.  tending  to  send  a  cur- 
rent through  the  leak  to  ground  would  be  the  difference 
of  potential  between  H  and  the  ground,  or  250  volts.  A 
man  standing  on  the  ground  at  H  and  coming  in  contact 
with  the  wire  would  be  subjected  to  a  pressure  of  250 
volts. 

240.  Arc  lights  are  sometimes  operated  on  constant- 
potential  circuits,  usually  at  from  110  or  220  volts 
pressure.  In  Fig..  75  ten  arc  lamps  are  represented  as 
being  connected  in  series,  and  the  extremities  of  the  cir- 
cuit are  assumed  to  be  connected  to  a  generator  directly. 
The  advantage  of  the  series  arc-circuit  is  a  high  pressure 
and  the  small  diameter  of  conductor  which  may  be  em- 
ployed for  conveying  the  total  strength  of  current,  usu- 
ally 10  amperes,  and  this,  in  a  district  of  street  lighting 
covering  an  extended  area,  is  a  matter  of  considerable 
importance.  The  advantage  of  multiple-arc  lighting  is 
found  in  the  combination  of  arc  lamps  with  incandescent 
lamps,  from  the  same  circuit,  without  additional  wires  or 
generators.  In  many  cases  it  is  more  economical  to  place 
arc  lights  on  already  existing  incandescent  circuits,  rather 
than  establish  entirely  separate  series-circuits  and  a  spe- 
cial generator,  even  though  the  amount  of  copper  re- 
quired in  the  circuits  be  considerably  increased.  This  is 
partly  on  account  of  the  increased  simplicity  of  the  sys- 
tem, the  reduced  space  and  cost  of  generators,  and  partly 


228 


on  account  of  the  greater  efficiency  of  incandescent  genera- 
tors. But  the  conditions  under  which  economy  exists  in 
the  use  of  constant  potential  arc  lamps  are  limited,  and 
each  case  must  be  determined  on  its  own  merits. 

Two  lamps  are  generally  operated  in  series  on  a  110 
volt  circuit,  and  four  lamps  in  series  on  220  volt  cir- 
cuit. A  small  resistance  is  usually  inserted  in  the  circuit 
of  each  lamp  to  assist  in  its  regulation.  The  usual  cur- 
rent strength  employed  in  constant-potential  lamps  is 
from  4  to  10  amperes.  The  best  results  are  obtained 
with  a  cored  carbon,  for  the  positive  electrode.  With 
the  usual  twelve  inch  positive  and  seven  inch  negative 
carbons,  of  ^  inch  diameter,  a  lamp  with  a  current  of 
nine  amperes  will  last  nearly  nine  hours. 

241.  Arc  lamps  are  sometimes  operated  from  special 
generators  on  alternating  current  circuits.  In 
such  cases,  since  the  carbons  are  alternately  positive  and 
negative,  neither  crater  nor  nipple  forms  on  the  car- 
bons, which  burn  with  comparatively  blunt  points.  In  the 
alternating  current  arc,  the  temperature  is  evenly  distri- 
buted; consequently,  the  horizontal  candle-power  does 
not  differ  so  markedly  in  intensity  from  the  maximum, 
and  there  are  two  directions  of  maxima,  one  upwards 
and  one  downwards,  as  shown  in  Fig.  76,  which  repre- 
sents in  polar  co-ordinates  the  distribution  of  light  in  a 
particular  case.  The  distribution  varies  considerably 
with  different  current  strengths  and  characters  of  carbon. 
Alternating  current  arcs  are  usually  operated  from  local 
step-down  transformers,  by  which  a  pressure  of  from  28 
to  35  volts  alternating  is  supplied  directly  to  the 
lamp  terminals.  The  current  in  the  main  or  primary  cir- 


cuit  of  the  generator  is  usually  about  30  amperes,  instead 
of  9  or  10,  as  in  the  continuous-current  circuit,  by  which 
means  a  lower  total  pressure  for  a  given  number  of  arcs 
can  be  obtained. 

242.     In  the  application  of  the  voltaic  arc  to  search- 
lights,   exceedingly   powerful   currents   are    em- 
ployed with  suitably  proportioned  carbons,  so  that  a  very 
great  intensity  of  light  is  obtained.     In  order  to  throw 


FIG.  76. 

Distribution  of  Light  from  an  Alternating  Current  Are  as  measured  in  a  particular  case. 

this  into  an  approximately  parallel  beam,  instead  of  dif- 
fusing it  in  all  directions,  the  carbon  arc  is  formed  at  the 
focus  of  a  suitable  projector.  These  projectors  may  be 
catoptric,  i.  e.,  reflecting ;  or,  dioptric,  that  is,  re- 
fracting. 

The  usual  form  is,  however,  a  reflector  of  the  parabolic 
or  spherical  type.  Since  large  parabolic  projectors  are 
very  expensive,  a  spherical  reflector  is  generally  em- 


230 


ployed.  This  consists  of  a  lens-shaped  mass  of  glass  the 
two  sides  of  which  have  different  radii  of  curvature,  the 
exterior  surface  being  silvered.  The  light  from  the  car- 
bon arc,  on  entering  the  substance  of  the  glass,  suffers  re- 
fraction, and  it  is  then  reflected  from  the  silvering  at  the 
exterior  surface  again  suffering  refraction  on  issuing 
from  the  glass  into  the  air.  The  curvatures  are  so  chosen 
with  regard  to  the  index  of  refraction  of  the  glass,  that 
the  light  emerges  in  a  sensibly  parallel  beam.  The  car- 
bons are  usually  tilted  at  such  an  angle  that  the  crater 


FIG.  77. 

Speciment  of  MagiuTtiu.  Reflector.     Section  through  Axis.    Dimensions  in  Centimetres. 

is  most  effectively  exposed  towards  the  reflecting  mechan- 
ism. In  many  cases  a  small  reflector  is  employed  near 
the  arc  to  throw  its  light  on  the  lens. 

The  beam  of  light  issuing  from  a  search  light  projector 
being  only  approximately  parallel,  necessarily  diverges 
and  lessens  in  intensity  with  the  distance  from  the  appa- 
ratus. Beyond  a  distance  of  a  few  hundred  feet,  the  illu- 
mination produced  by  the  beam  approximately  varies 
inversely  as  the  square  of  the  distance.  Neglecting,  how- 


231 


ever,  the  absorption  of  light  by  dust  and  fog  in  the  at- 
mosphere, the  total  flux  of  light  in  the  beam  remains 
constant,  so  that  the  area  of  the  beam  increases  after  the 
flrst  few  hundred  feet  approximately  as  the  square  of  the 
distance. 

A  Mangin  reflector  is  represented  in  axial  section  in 
Fig.  77.  The  arc  being  placed  at  the  principal  focus 
A,  which  in  this  case  is  38.3  cms.  from  the  centre  of 
the  inner  surface,  throws  a  beam  parallel  to  p  A,  of  dia- 
meter D  E,  the  surface  B  o.c,  being  silvered. 

243.  Carbon  arc  lights  for  street  lighting  are  gener- 
ally surrounded  by  globes,  which  may  be  clear  or 
ground.  In  either  case  a  loss  of  light  is  thereby  entailed, 
but  a  more  uniform  diffusion  of  light  obtained.  This  is 
especially  the  case  where  the  globe  is  ground  or  consists 
of  translucent  glass  or  porcelain.  The  loss  of  light  may 
amount  to  as  much  as  60  per  cent.,  but  the  general  illu- 
mination produced  is  better  and  shadows  are  avoided. 


SYLLABUS. 

Arc  lights  are  generally  operated  commercially  on 
series  circuits  from  specially  designed  dynamos,  generat- 
ing sufficient  difference  of  potential  to  maintain  the  cur- 
rent constant  under  all  conditions.  Arc  lamps  are  some- 
times operated  on  constant-potential  circuits,  with  either 
two  or  four  lamps  in  series. 

Arc  lamps  are  sometimes  operated  on  alternating-cur- 
rent circuits  from  transformers. 


232 


Alternating-current  lamps  have  two  maxima  of  light 
intensity,  one  upwards  and  one  downwards,  no  marked 
crater  being  formed. 

Reflectors  are  commonly  used  with  large  search  lights. 

Globes  placed  around  arc  lights,  while  useful  for  dif- 
fusing the  light,  cut  off  from  10  to  60  per  cent  of  the 
total  light  emitted. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINEER.] 
WEEKLY. 

No.  30.  JANUARY  5,  1895. 

Electrical    Engineering   Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED      GRADE. 

Alternating  Currents 


The  comprehension  of  the  following  definitions 
is  necessary  to  a  clear  understanding  of  alternat- 
ting  currents. 

An  alternating  E.  M.  F.  or  current  is  an  E.  M.  F.  or  cur- 
rent which  successively  reverses  its  direction. 

Fig.  78  is  a  graphical  representation  of  an  E.  M.  F. 
or  current  which  is  alternating,  for  it  successively  changes 
its  sign,  being,  say,  in  the  positive  direction  at  a,  and  in 
the  negative  direction  at  0,  while  at  b  df  h  &,  it  has  zero 
value  and  no  direction. 

Aperiodic  alternating  E.  M.  F.  or  current,  is  an  alter- 
nating E.  M.  F.  or  current  which  not  only  periodically 
reverses  its  direction,  but  also  periodically  repeats  its 
changes  in  magnitude.  Figs.  79  to  84  represent  periodic 
alternating  E.  M.  F.'S  or  currents. 

The  terms  alternating  E.  M.  F.,  or  alternating  current, 
as  ordinarily  employed,  designate  periodic  alternating 
E.  M.  F.  and  current,  respectively. 

Published  by 

THE  ELECTRICAL  ENGINEER, 
303  Broadway,  New  York,  N.  Y. 

[Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  June  14,  1804.] 


234 


Each  reversal  of  a  periodic  alternating  E.  M.  F.  or  cur- 
rent is  called  an  alternation  or  semi-period.  Thus  in 
Fig.  79,  o  a  I  c,  or  c  d  <?/*,  orj  k  I  m,  each  represent  one 
alternation  or  semi-period. 


i    i 

Elec.  Engineer 


FIG.  78. 

Graphical  Representation  of  Non  Periodically  Alternating  Current  or  E.  M.  F. 

A  complete  doable  alternation  or  double  reversal  is 
called  a  cycle.  Thus  in  Fig.  80,  the  curve  oab  cd  efg  A, 
represents  one  double  reversal  or  cycle.  It  is  not  neces- 
sary, however,  that  the  cycle  commence  at  the  zero  point. 
Thus  cdefghjkl,  mfghjkl  mnp,  each  represent 
one  cycle. 

The  time  occupied  in  executing  a  cycle  is  called  a 
period.  Thus  in  Fig.  79,  the  period  is  0.01  second.  In 


c 

f 

j 

m        |, 

§ 

« 

I          e 

•      ft 

j 

FIG.  79. 

Periodic  Alternating  E.  M.  F.  or  Current. 
Rectangular  Type. 


Elec.  Engineer 

FIG.  81. 

Periodic  Alternating  E.  M.  F.  or  Current. 
Zig-zag  Type. 


Fig.  80  the  period  is  0.1  second,  and  in  Fig.  82,  0.004 
second. 

The  number  of  periods  described  in  one  second,  or 
the  reciprocal  of  the  period,  is  called  the  frequency. 


23-5 


245.     Thus  in  Fig.  79,  the  frequency  is  100 

is,  100  periods  per  second  ;  in  Fig.  80,  10 
in  Fig.  82,  250  ~. 


that 
and 


FIG.  80. 

Periodic  Alternating  E.  M.  F.  or  Current.     Circular  Type. 

When  the  E.  M.  F.  or  current  periodically  reverses,  it 
may  do  so  in  an  infinite  variety  of  ways  ;  namely, 

(1.)  It  may  change  suddenly  from  the  positive  maxi- 
mum value  to  the  negative  maximum  value,  and  vice 
versa,  as  shown  in  Fig.  79.  The  graphical  representation 
of  these  reversals  is  a  rectangular  curve. 

(2.)  It  may  change  gradually  from  the  positive  maxi- 
mum value  to  the  negative  maximum  value  and  vice 
versa,  as  shown  in  Fig.  81. 

(3.)  It  may  change  from  the  full  positive  value  to  the 
full  negative  value  according  to  a  definite  law,  more 


FIG.  82. 

Periodic  Alternaling  E.M.F, 

or  Current. 
Flat-Topped  Curve. 


FIG.  83. 

Periodic  Alternating  E.M.F. 

or  Current. 
Peaked  Curve. 


FlG.  84. 

Periodic  Alternating  E.M  F 

or  Current. 
Sinusoidal  Curve. 


complex  than  either  (1)  or  (2).  Such  changes  are  shown 
in  Figs.  78,  82,  83  and  84.  Thus,  Fig.  78  represents 
graphically  a  circular  variation  or  type  of  wave  ;  Fig. 


236 


82,  a  flat-top  type  of  wave  ;  Fig.  83,  a  peaked  type  of 
wave  and  Fig.  84,  a  sinusoidal  wave. 

246.     A  sinusoidal  E.  M.F.  or  current  is  one  whose  suc- 
cessive magnitudes  with  respect  to  time  vary  as  the 
sine  of  a  quantity  proportional  to  the  time,  or  which 
alternates  in  time  according  to  a  simple  harmonic  law. 


.Elec.Eny  tnvt>r 

FIG.  85. 

Graphical  Representations  of  Simple  Harmonic  E.  M.  F.'S  or  Currents. 

An  example  of  a  simple-harmonic  motion  (abbreviated 
s.  H.  M.)  is  seen  in  the  motion  of  a  vertically  falling  shadow 
projected  upon  a  horizontal  plane,  from  a  point  on  a  verti- 
cal disc  which  is  uniformly  rotating  about  a  horizontal 
axis.  Thus  in  Fig.  85,  the  disc  Q  K  s,  revolving  uniformly 
about  its  horizontal  axis  at  o,  has  a  pin  p,  whose  shadow 


237 


falling  vertically  upon  a  band  of  paper  T  v,  lying  in  a 
horizontal  plane,  produces  an  s.  H.  M.  upon  the  paper.  If, 
therefore,  the  paper  be  moved  in  the  direction  of  the 
arrow  in  its  own  plane  and  in  a  direction  at  right  angles 
to  the  plane  of  the  disc,  the  shadow  will  trace  on  the 
paper  a  simple-harmonic  or  periodic  curve,  A  B  c  D  E  F, 
and  this  curve  is  called  sinusoidal,  because  any  ordinate, 
such  as  o  A,  is  proportional  to  the  sine  of  the  angle  con- 
tained between  the  radius  of  the  pin  and  the  vertical 
plane  through  the  axis  of  the  disc.  It  is  evident  that 
the  outline  of  the  sinusoidal  curve  so  traced  depends 
upon  the  distance  of  the  pin  from  the  axis,  and  the 
velocities  of  disc-rotation  and  paper-progression.  Thus, 
assuming  the  paper  to  move  with  the  same  velocity  in 
the  four  cases  represented  at  A,  B,  (7 and  D,  respectively, 
then  the  shape  of  the  curve  will  only  depend  upon  the 
position  of  the  pin  and  on  the  velocity  of  its  rotation. 
Thus,  the  pin  is  shown  in  the  same  position  at  A,  and  at 
D,  namely,  near  the  edge  of  the  disc ;  but  since  the 
velocity  of  rotation  at  D,  is  twice  that  at  A,  the  cycle  is 
completed  in  half  the  time  at  J9,  and  the  frequency  of  the 
periodic  motion  is,  therefore,  twice  as  great  at  D,  as  at  A. 
At  B  arid  (7,  the  pin  is  shown  half  way  between  the  centre 
and  the  edge  of  the  disc,  while  (7,  has  twice  the  rotary 
velocity  of  B.  The  amplitude  or  maximum  ordinate 
in  B  and  C,  is  half  that  in  A  and  D.  The  frequencies 
in  O  and  D  are  equal,  and  the  frequencies  in  A  and  B,  are 
equal.  The  waves  represented  at  A,  B,  6y,  or  D  are,  there- 
fore, all  sinusoidal  waves  in  spite  of  their  differences  of 
appearance,  and  any  E.  M.  F.'S  or  currents,  whose  suc- 
cessive changes  in  time  are  represented  by  such  curves 
are  sinusoidal  E.  M.  F.'S  and  currents. 


288 


Calling  £,  the  time  in  seconds  dating  from  the  initial  or 
zero  position,  to,  the  angular  velocity  of  the  disc  in  radi- 
ans per  second,  and  Y,  the  amplitude,  the  y — ordinate  at 
any  instant  is  y  =  Y  sin  co  t. 

The  angle  contained  between  the  radius  vector  o  P, 
and  the  initial  ascending  vertical  radius  o  K,  is  called  the 
phase  of  the  motion.  Thus  the  phase  of  the  point  c,  in 
the  curve  of  A9  is  270°,  the  phase  of  the  point  E,  90°  and 
of  B  and  F,  zero. 

247.  A  coil  of  insulated  wire,  rotated  with   uniform 
velocity  about  any  diameter  as  axis  in  a  uniform 

magnetic  flux,  has  generated  in  it  a  sinusoidal  E.  M.  F."  In 
practice  alternators,  or  dynamos  for  producing  alternating 
E.  M.  F.'S,  never  produce  strictly  sinusoidal  E.  M.  F.'S,  al- 
though they  frequently  generate  E.  M.  F.'S  that  are  suf- 
ficiently nearly  sinusoidal  to  be  considered  as  true  sinu- 
soids for  purposes  of  computation.  The  E.  M.  F.  gen- 
erated by  any  practical  alternator  may  be  regarded  as 
lying  between  the  flat-topped  type  of  Fig.  82  and  the 
peaked  type  of  83. 

248.  Since  an  E.  M.  F.  or  current  which  is  changing 
its  direction  many  times  a  second,  has,  at  different 

instants  of  time,  all  values  comprised  between  its  maximum 
and  zero,  it  becomes  necessary  to  define  conventionally 
the  numerical  value  of  such  an  E.  M.  F.  or  current.  If  this 
value  were  taken  as  being  equal  to  the  maximum,  the 
E.  M.  F.  or  current  could  only  attain  its  nominal  value  twice 
in  each  cycle.  If  the  arithmetical  mean  value  without  re- 
gard to  sign  be  taken,  the  value  so  obtained  is  called 
the  mean  E.  M.  F.  or  mean  current  but  this  value  has 
very  little  practical  application.  The  value  of  an  alter- 


nating  E.  M.F.  or  current  is  most  conveniently  defined 
by  reference  to  its  heating  power  and  this  is  the  method 
invariably  adopted.  If  a  given  continuous-current  pres- 
sure maintains  a  given  thermal  activity  in  a  fixed  resist- 
ance, then  the  alternating  E.  M.  F.,  which  will  maintain 
the  same  thermal  activity  in  the  resistance,  will  have  the 
same  nominal  val  lie  expressed  in  volts,  so  that  this  value, 
which  is  called  the  effective  value  of  the  E.  M.  F.,  may  be 
regarded  as  the  value  of  the  continuous  E.  M.  F.  required 
to  produce  the  same  thermal  activity.  Since,  according 
to  Ohm's  law,  the  thermal  activity  maintained  in  a  re- 

<?2 
sistance  R,  by  an  unvarying  E.  M.  F.  of  ^  volts,  is  -^ 

watts,  the  activity  developed  by  a  periodically  varying 

E.  M.  F.,  at  any  instant,  will  be  similarly  ^  watts,  where 

H 

e,  is  the  instantaneous  value  of  the  E.  M.  F.  The  value  of 
e\  if  averaged  over  a  sufficiently  long  time,  will  corres- 
pond to  the  square  of  the  effective  E.  M.  F.  e^  or  in  mathe- 
matical language,  if  E,  be  the  effective  E.  M.  F., 


where  r,  is  the  time  occupied  in  any  complete  cycle.  In 
the  case  of  a  sinusoidal  or  simple  harmonic  E.  M.  F.,  the 
effective  E.  M.  F.  is  always  the  maximum  E.  M.  F.  in  the 
cycle  divided  by  -v/2?  so  that  the  effective  E.  M.  F.  = 
0.7071  maximum  E.  M.  F. 

SYLLABUS. 

A  sinusoidal  E.  M.  F.  or  current  is  one  whose  successive 
magnitudes  with  respect  to  time  are  represented  by  the 
ordinates  of  a  sinusoidal  or  simple-harmonic  curve. 


240 

~No  alternators  generate  strictly  sinusoidal  E.  M.  F.'S, 
but  many  generate  E.  M.  F.'S  which  are  sufficiently  nearly 
sinusoidal  to  be  regarded  as  such  for  purposes  of  com- 
putation. 

The  effective  value  of  an  alternating  E.  M.  F.  or  current 
is  the  square  root  of  the  time  average  of  its  square. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINBBR.] 
WEEKLY. 


No.  31.  JANUARY  12,  1895. 

Electrical   Engineering  Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED      CRADE. 

Alternating  Currents. 


249.  When  two  simple  harmonic  E.  M.  F.'S,  of  the 
same  frequency,  are  simultaneously  impressed  on 

the  same  circuit  in  series,  as,  for  example,  when  two 
similar  alternators  are  driven  on  the  same  shaft,  the 
effect  produced  will  depend  upon  the  relative  phases  of 
the  two  E.  M.  F.'S  ;  for,  if  the  two  E.  M.  F.'S  are  in  phase 
their  combined  effect  or  resultant  will  be  equivalent  to 
their  arithmetical  sum,  or  to  that  of  a  single  source  of 
double  E.  M.  F.  If,  however,  the  two  E.  M.  F.'S  are  in 
opposite  phase,  their  resultant  will  be  zero,  and  between 
these  two  conditions  there  will  be  an  infinite  number  of 
possible  intermediate  resultants.  In  all  cases,  however, 
the  sum  of  their  E.  M.  F.'S  will  be  their  vector  or 
geometrical  sum. 

250.  In  order  to  determine  the  value  of  the  sum  of  two 
or  more  vectors  in  a  plane  we  proceed  as  follows. 

Let  A  B,  be  a  quantity  whose  magnitude  and  direction  are 
represented  by  the  line  A  B,  Fig.  86,  and  let  o  D,  be  a 

Published  by 

THE  ELECTRICAL  ENGINEER, 
203  Broadway,  New  York,  N.  Y. 

[Entered  as  second-class  matter  atjthe]  New  York,  N.  Y.,  Post  Office,  June  14,  1804.] 


242 


quantity  whose  magnitude  and  direction  are  represented 
by  the  line  c  D  ;  then  the  vector  sum  of  A  B  and  c  r>, 
will  be  found  by  laying  off  from  B,  a  line  parallel  to  and 


Elec.Engineer 

FIG.  86. 

equalto  c  D,  so  that  the  straight  line  A  D,  will  be  the 
vector  sum.  If  now  A  B,  represents  at  some  instant  of 
time  the  relative  position  of  the  sinusoidal  E.  M.  F.,  of 
say  1180  volts  effective,  a  second  sinusoidal  E.  M.  F. 
of  say  820  volts  effective,  whose  phase  is  150°  in  rear 
of  A  B;  i.e.,  T5^  of  a  complete  revolution,  or  period,  will 
be  represented  by  c  D.  For  if  the  lines  A  B  and  c  D,  be 
each  set  revolving  counter-clockwise  about  the  ex- 
tremities A  and  c,  respectively,  with  equal  and  uniform 
angular  velocities  in  the  plane  of  the  paper,  then  if  c  D, 
lags  150°  behind  A  B,  when  A  B,  reaches  the  position 
shown  CD,  will  also  occupy  the  position  indicated.  Their 
vector  sum  A  D,  will  be  the  resultant  or  combined  E.  M.  F. 
of  these  two  generators  when  placed  in  series  at  this  de- 


,   K 


PIG.  87. 

finite  phase  relationship  and  will  be  represented  by  a 
sinusoidal  E.  M.  F.  of  620  volts  effective,  41°  behind  A  B. 
If,  as  represented  in  Fig.  87,  two  equal  sinusoidal 


243 


E.  M.  F.'S,  each  1000  volts  effective,  are  connected  in 
series  at  an  angle  of  60°,  or  ^  period,  their  resultant  will 
be  a  sinusoidal  E.  M.  F.  of  1733  volts.  T^  period  ahead  of 
E  F,  or  y1^  period  behind  F  G.  If  the  angular  displace- 
ment be  J  period,  their  resultant  will  be  1415  volts 
effective,  -J  of  a  period  later  than  j  K  ;  while,  if  the 
angular  divergence  be  150°,  their  resultant  will  be  518 
volts  effective,  75°  in  advance  of  L  M. 

Any  number  of  co-periodic  simple  harmonic  E.  M.  F.'S 
can  be  compounded  into  an  equivalent  single  resultant  by 
finding  their  vector  sum. 


E 

62  VOLTS 


t 


^ 


RESISTANCE   10  OHMS 


FIG.  88.  FIG  89. 

The  impressed  E.  M.  F.  at  the  terminals  of  an  alternat- 
ing current  circuit  is  always  equal  to  the  geometrical 
sum  of  the  component  c.  E.  M.  F.'S  in  that  circuit,  that  is 
to  say,  if  there  be  only  resistance  in  the  circuit,  the  im- 
pressed E.  M.  F.  will  be  expressed  by  the  c.  E.  M.  F.,  /  R  ; 
or,  if  there  be  additional  c.  E.  M.  F.'S  of  the  type  0,  the 
impressed  E.  M.  F.  will  be  expressed  by  the  vector  sum 
Ifi  +  e. 

This  law  applies  to  the  continuous  current  circuit 
where  however  the  sum  is  merely  arithmatical. 

If,  therefore,  the  drop  /  7?,  in  the  resistance,  be  laid 
off  on  the  line  A  B,  Fig.  88  and  the  c.  E.  M.  F.,  0,  due  to 
the  variation  of  flux  linkage  be  laid  off  by  the  line  B  c, 
at  right  angles  to  A  B,  and  90°  in  advance  of  it,  then  A  c, 


244 


will  be  the  vector  sum  of  the  c.  E.  M.  F.'S,  and  this  must 
be  equal  to  the  impressed  E.  M.  r. 

251.  Instead  of  considering  the  current  produced  in 
an  alternating-current  circuit  as  being  numerically 
equal  to  the  quotient  of  the  resultant  E.  M.  F.  by  the 
ohmic  resistance  of  the  circuit,  in  accordance  with  Ohm's 
law,  it  is  frequently  simpler  to  regard  the  impressed 
E.  M.  F.  as  acting  alone  in  the  circuit,  and  that  the  resist- 
ance of  the  circuit  is  altered  to,  what  is  called  the  impe- 
dance of  the  circuit.  For  example,  if  the  circuit 
possesses  a  resistance  a  5,  Fig.  89  of  say  10  ohms,  and 
the  frequency  of  the  E.  M.  F.  be  100  ^,  its  angular 
velocity  will  be  628.3  radians  per  second ;  i.e.  the  angu- 
lar velocity  of  the  revolving  line  in  the  plane  of 
the  paper  will  be  100  X  2  TT.  If  the  inductance  be 
0.015  henry,  the  reactance  I  c,  will  be  0.015  X  628.3  = 
9.425  ohms,  90°  in  advance  of  a  &,  and  the  impedance  of 
the  circuit  will  be  the  geometrical  sum  of  these  two 
components,  or  a  c,  13.74  ohms,  43°  18'  in  advance  of 
a  b.  We  have,  therefore,  in  an  alternating  current  cir- 
cuit, the  vector  relationships, 

(1)  Reactance  of  an  Inductance  L  henrys  =  j  2  TT  n  L 
ohms  where  n,  is  the  frequency  and  j,  is  the  symbol  of 
direction  or  V--  1,  indicating  that  the  reactance  is  set 
at  right  angles  to  the  resistance. 

(2)  Impedance  =  Resistance  -f-  Reactance.      Ohm's 

T? 

law   applied    to    such   a   circuit    becomes   /  =  _  am- 

J 

peres,  where  «/,  is  the  vector  impedance.  In  dividing 
vectors,  their  lengths  are  divided  numerically  and  their 
angles  subtracted.  Thus,  if  p  Q,  and  E  s,  Fig.  90  be  two 
vectors  p  Q,  being  0.8  /60°,  and  R  s,  0.5  /270°;  or, 


245 

0.5  \  90°,  their  arithmetical  product  will  be  0.8  X  0.5 
/270°  +  60°   =   0.4  /33Q°'  =   0.4     \30.     While   the 

quotient  of  If  =  will  be  -8  /60  —  270  =  1.6  /—  210 
R  s  0.5  


=  1.6  \  210  =  1.6/150°  as  shown  at  T  v,  and  v  w,  Fig. 
90.  If  then,  the  resistance  coil  last  considered,  have 
an  impressed  sinusoidal  E.  M.  F.  of  say  52  volts,  con- 
nected to  its  terminals,  the  current  in  the  circuit  will  be 

M  3.785 

13.74  ,/43°  IS'  :  "  /43°  18' 

as  represented  in  Fig.  89,  and  the  current  will,  there- 
fore, lag  43°  IS'  behind  the  E.  M.  F.  in  phase. 


252.  The  reactance  of  a  condenser  is  the  reciprocal 
of  the  product  of  its  capacity  in  farads  and  the 
angular  velocity  of  the  impressed  E.  M.  F.  Thus,  if  a 
condenser  of  10  microfarads ;  that  if,  10~5  farad,  be  con- 
nected directly  with  the  terminals  of  the  alternator  of 
100  ~,  and  1100  volts  effective,  as  measured  at  ter- 
minals, the  reactance  of  the  condenser  at  this  frequency 

will  be =  159.2  ohms  ;  but  this  reactance, 

10-5  X  628.3 

while  set  off  at  right  angles  to  ohmic  resistance,  is  marked 
in  the  opposite  direction  to  inductance-reactance  as  shown 


246 


at  B  G  Fig.  91.  This  is  for  the  reason  that  inductance 
and  capacity  in  a  circuit  tend  to  neutralize  each  others 
influence,  and,  calling  the  inductance-reactance  positive, 
capacity-reactance  is  reckoned  as  negative.  The  current 
through  the  condenser  under  these  conditions  will  be 

_  —  6.91  /90°.  so  that  the  current  in  this  case 
159.2  \  90° 

leads  the  E.  M.  F.  by  a  quarter  period.     The  reactance  of 

a  condenser  of  capacity  c,  farads  is  therefore  —  j  — 

'   .<?  a) 

ohms,  where  a)  =  2  n  n,  the  angular  velocity. 


II 


FIG.  91. 

The  drop  in  a  resistance  in  a  continuous  current  cir- 
cuit is  1  R,  volts.  The  drop  in  the  impedance  of  an 
alternating  current  circuit  is  /  «/,  volts. 

Let  for  example,  a  coil  of  50  ohms  have  an  inductance 
of  0.02  henry  (20  milli-henrys)  and  be  connected  in 
series  with  a  condenser  of  10  micro-farads  capacity  to 
the  terminals  of  a  sinusoidal  alternator  delivering 
1100  volts  effective  at  a  frequency  of  100  ~.  The  re- 
actance of  the  condenser  will  be  —  159.2  ohms  as  be- 
fore. The  reactance  of  the  inductance  in  the  coil  will 
be  628.3x0.02  =  125. 7  ohms,  and  the  resultant  reactance 
—  33.5  ohms  as  shown  in  Fig.  92.  The  impedance,  or 


247 


resultant  of  the  reactance  and  resistance,  will,  therefore, 
be  60.2  ohms  and  the  current  in  the  circuit  will    be 

.  —  18.27  /33°  50'  amperes,  so  that  a  cur- 
60.2  \  33°  50' 

rent  of  18.27  amperes  .effective,  leads  the  E.  M.   F.  by 
approximately  34°. 

The  drop  at  the  terminals  of  the  condenser  will  be 
18.27  /33°  50'  X  159.2  \  90°  =  2909  \  56°  10'  volts. 
The  drop  in  the  inductance  if  it  could  be  isolated ;  that 


"'  50  OHMS** 


FIG.  92. 


FIG.  93. 


FIG.  94. 


is,  separated  from  the  resistance  in  the  coil  would  be 
18.27  /33°  50X  X  125.7  /90°  =  2296  /123°  50r  volts, 
and  tlie  drop  in  the  resistance  18,27  /33°  50'  X  50  = 
913.5  /33°  50X  volts.  As,  however,  the  inductance  and 
the  resistance  in  a  coil  are  inseparably  united,  the  drop 
can  only  be  measured  on  the  impedance  of  the  coil, 
which  will  be  50-|-125.7>;  =  135.3  ohms,  as  shown  in  Fig. 


248 


93,  j,  being  the  symbol  of  V  —  1  or  an  operator  which 
rotates  125.7  through  a  right  angle,  counter-clockwise 
from  the  direction  of  the  resistance.  The  drop  at  the 
terminals  of  the  coil  will,  therefore  be  18.27  /33°  50'  X 
135.3  /68°  19r  =  2472  /1Q2°  09',  and  as  shown  in  Fig.  94 
2472  /102°  09;  +  2909  \  50°  10'  =  1100. 

It  is  evident  that  by  the  combination  of  an  induct- 
ance with  a  condenser,  the  pressure  at  the  terminals  of  a 
condenser  may  exceed  that  of  the  impressed  E.  M.  F. 
The  vector  sum  of  the  total  c.  E.  M.'F.'S  or  drops  in  the 
circuit  must,  however,  be  equal  to  the  impressed  E.  M.  F. 
as  shown  in  Fig.  94. 

If  the  reactance  of  a  condenser  is  equal  to  the  react- 
ance of  the  inductance  in  a  circuit,  the  impedance  of  the 
circuit  is  reduced  to  its  simple  resistance,  so  that  an  al- 
ternating current  circuit  on  a  coil  having  a  small  resist- 
ance but  large  inductance,  in  circuit  with  a  properly 
selected  condenser  may  develop  an  exceedingly  high 
pressure  at  the  condenser  and  at  the  coil  terminals.  Such 
a  circuit  is  said  to  be  resonant. 

SYLLABUS. 

The  sum  or  difference  of  two  co-periodic,  sinusoidal 
E.  M.  F.'S  is  their  geometrical  or  vector  sum,  or  differ- 
ence. 

Laboratory  of  Houston  &  Keiinelly, 
Philadelphia. 


[Copyright,  1894,  by  THE  ELECTRICAL  ENGINBBR.] 
WEEKLY. 


No.  32.  JANTTAHV  19,  1895.        l^tio"  S3m 

Electrical    Engineering   Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED 

Alternating  Currents. 


253.     Since  in  an  alternating-current  circuit  we  have 

Tf  1 

the  vector  equation  I  =  —  amperes  =  E  .-  .am- 

J  J 

peres,  we  may  write  1  =  E  A  amperes,  where  the  ad- 
mittance A,  is  the  reciprocal  of  the  impedance,  and  is 
expressed  in  mhos.  In  a  continuous-current  circuit, 

7? 

I  =  —  =  E  G  amperes,  where  6r,  is  the  conductance  in 
R 

mhos  (Sec.  24),  and  the  admittance  A,  degrades  into  a 
simple  conductance. 

In  a  continuous-current  circuit,  the  joint  conductance 
of  a  number  of  separate  conductances  in  multiple  is  their 
arithmetical  sum. 

In  an  alternating -current  circuit,  the  joint  admittance 
of  a  number  of  separate  admittances  in  multiple,  is  their 
geometrical  sum.  For  example,  let  two  impedances  be 
connected  to  the  terminals  of  an  alternator  delivering 
1100  volts  at  coJJ.es tor  rjpgs,  with  a  frequency  of  12S  *v, 

Published  by 

THE  ELECTRICAL  ENGINEER, 
203  Broadway,  New  York,  N.  Y. 

[Entered  &  second-cla«s  matter  at  the  New  York,  N.  Y.,  Port  Office,  June  14,  1894.  ] 


250 


one  of  these  impedances  being  offered  by  a  coil  of  30 
ohms  resistance  and  0.2  henry  inductance,  and  the 
other  impedance  being  that  of  a  condenser  of  10  micro- 
farads capacity ;  then  the  angular  velocity  of  the  E.  M.  F.  is 
785.4  radians  per  second.  As  shown  in  Fig.  95,  the  re- 
actance of  the  inductance  is  15 Y.I  /90°  ohms,  and  the 
impedance  C  E,  159.9  /79°  11'  ohms.  The  reactance 


it  \° 
°i  / 


C  80  OHMS  D 


"0.002076  MHO 


FIG.  95. 

Illustrating  the  Combination  of  Impedances  in  Parallel. 


of  the  condenser  is  127.3  \  90°  ohms,  and  this,  in  the 
absence  of  resistance  in  series  with  it,  becomes  its  im- 
pedance. The  admittance  of  the  coil  is,  therefore 

159  9  /79°  11'  =  °-006252  \  W°  H'  raho,  as  repre- 
sented by  the  line  c  d,  to  a  convenient  scale ;  and  the 
admittance  of  the  condenser  is  similarly  —— — ===^ 

4.27.0  \  yo 


251 


=  0.007854  /90°  mho.  The  geometrical  sum,  or  joint 
admittance  of  a  I  and  c  d,  is  a  d,  0.002076  /55°  37' 
mho.  The  joint  impedance  is,  therefore 


0.002076 


\55 


as  represented  by  the  line  G  H,  to  a  suitable  scale.  The 
current  supplied  from  the  alternator  will,  consequently 

be  -  =  =  2.284  /55°  37'  amperes,  as  shown 

"  481.6  \  55°  37' 
by  the  line  N  p.     The  current  in  the  resistance  coil  will 

be  159  9  7790  n/  =  6.877  \  79°  11'  amperes,  as  repre- 
sented by  the  line  L  M,  and  the  current  in  the  condenser 

will  be  —  —          o  =  8.641  /90°  amperes,  as  shown  by 
\2ii.o  \  90 

the  line  j  K.  The  arithmetical  sum  of  these  two  branch 
currents  would  be  6.877  +  8.641  =  15.518  amperes, 
whereas  the  current  actually  supplied  is  only 
2.284  /55°  37'  amperes,  and  this  is  the  vector  sum  of 
6.879  /79°  11'  +  8.641  /90°. 

254.  In  a  continuous-current  circuit  we  have  the  con- 
dition that  the  sum  of  tfre  currents  arriving  at  a 
point  in  a  network  of  conductors  is  equal  to  the  sum  of 
the  currents  leaving  that  point  (Sec.  50).  This  is  true 
in  an  alternating  current  circuit  if  we  substitute  the 
geometrical  sum  for  the  arithmetical  sum. 

The  multiplying  power  of  a  shunt  (Sec.  37)  in  a  con- 

S7          I          & 

tinuous  current  circuit  is  -  '  T*  '  ?  where    G,  is  the  re- 

X3 

sistance  of  the  galvanometer  or  similar  device,  and  /£, 


252 


the  resistance  of  the  shunt.  In  an  alternating-current 
circuit,  the  same  ratio  holds  when  the  computation  is 
effected  geometrically.  Thus,  suppose  a  galvanometer 
applicable  to  an  alternating-current  circuit ;  for  instance, 
an  electro-dynamometer  is  placed  in  a  circuit  whose  fre- 
quency is  125  ~,  and  whose  angular  velocity  is  there- 
fore, 785.4  radians  per  second,  with  a  resistance  of  6.19 
ohms,  and  an  inductance  of  0.01  H.  Its  reactance, 
therefore  will  be  7.854  ohms,  and  its  impedance,  as 
shown  in  Fig.  90  of  10  /51°  45'  ohms.  If  this  dynamo- 
meter is  shunted  by  a  simple  non-inductive  resistance  $, 
of  10  ohms,  and  whose  impedance  is,  therefore,  10  /0° 


100HM8. 


FIG  96. 

Illustrating  the  Multiplying  Power  of  a  Shunt. 

ohms,  then  the  vector  sum  G  -\-  $,  is  shown  to  be 
17.99  /25^3/  ohms.  This  sum  divided  by  8,  is  clearly 
1.799  /25°  53',  so  that  the  readings  of  the  dynamometer 
would  have  to  be  multiplied  by  1.799  in  order  to  obtain 
the  total  current  strength. 

255.  In  the  same  way  it  may  be  shown  that  all  the 
formulae,  applying  to  continuous-current  circuits^ 
apply  equally  to  sinusoidal-current  circuits  when  the 
proper  impedances, are  substituted  for  the  various  re- 
sistances, and  the  computation  is  carried  out  vectorially. 

In  a   continuous-current  circuit,  the  activity  is   E  1 


253 


watts,  E  I,  being  the  numerical  product.  In  a  sinusoidal- 
current  circuit,  the  activity  is  E  /watts,  E  1,  being  in- 
terpreted geometrically,  and  representing  the  co-directed 
product ;  or,  if  «,  be  the  angle  included  between  E,  and 
/,  the  activity  is  E  /cos  a  watts. 

Thus,  considering  the  case  represented  in  Fig.  95,  the 
activity  supplied  to  the  condenser  by  the  alternator  of 
1100  volts,  will  be  1100  X  8.641  X  cos  90°  =  0,  (see 
Fig.  97.)  Such  a  current  is  sometimes  called  a  wattless 
current. 


_    .  ^A™— >- 

,100  VOLTS          B,  A,,  1100  VOLTS  Bw 

£2ec-Engineer 


FIG.  97. 

Illustrating  Activity  Relations. 

Considering  next  the  activity  in  the  circuit  of  the  coil, 
we  have  1100  X  6.877  X  cos  79°  IV  =  1419  watts. 
This  energy  is  expended  in  heating  the  coil. 

256.  When  the  circuit  embraces  iron,  there  will  be 
hysteretic  expenditure  of  energy  in  the  iron  at 
each  cycle  (Sec.  148).  The  effect  of  the  hysteresis  will 
be  to  apparently  increase  the  resistance  in  the  circuit,  to 
what  may  be  termed  its  equivalent  resistance.  Thus,  if 
an  E.  M.  F.  of  100  volts  at  130  ~  be  impressed  upon  the 
terminals  of  a  coil  embracing  iron,  having  a  resistance  of 
1.0  ohms  (Fig.  98)  and  an  inductance  of  0.1  henry  (sym- 
bolically written  0.1  H\  the  angular  velocity  being 


254 


816.8  radians  per  second,  the  reactance  of  the  coil  will 
be  81.68  /90°  ohms,  and  the  impedance  of  the  coil  will 
be  82.31  /83°  01'  ohms.  If,  owing  to  the  effect  of 
hysteresis,  the  100  volts  is  opposed  by  a  c.  E.  M.  F.  20 
/1  50°  volts,  as  shown  by  the  line  E  F,  the  resultant  E.  M.  r. 
will  be  D  E  +  E  F,  or  83.28  /6°  54'  volts,  and  this  re- 
sultant E.  M.  F.,  considered  as  acting  on  the  impedance  of 

83  28 
' 


the  coil,  will  produce  a  current 


82  31  ,^go  01/ 


\  83°  01'  amperes,  represented  by  the  line  d  g,  which 


*k       d\—~i—---  esi'^ 

'     83,%,'  76°07/       - 


Elec.Engineer 


FIG.  98. 

Illustrating  Equivalent  Resistance,  Reactance  and  Impedance. 

will  be  76°  07'  behind  the  impressed  E.  M.  F.  d  19  of  100 
volts.  The  same  result  can,  however,  be  obtained  if  we 
consider  the  impressed  E.  M.  F.  as  acting  directly  on  a 
circuit  whose  impedance  is  98.8  /76°  07'  ohms,  and  whose 
equivalent  resistance  and  reactance  are  23.7  ohms,  and 
95.96  /9^  ohms,  respectively. 

257.     The  ratio  of  the  impedance  to  the  ohmic  resis- 

tance in  a  conductor  or  circuit  is  called  its  im- 

pedance factor.    The  ratio  of  the  reactance  to  the  ohmic 


255 


resistance  in  a  conductor  or  circuit  is  called  its  reactance 
factor.  The  impedance  factor  is  therefore  the  secant, 
and  the  reactance  factor  the  tangent,  of  the  angle  of  lag. 

258.     When  an  alternating  current  in  a  primary  circuit 

is  linked   with  a  secondary  circuit,  through  the 

medium  of  a  mutual  inductance  of  L^  henrys,  an  E.  M.  F. 

is  set  up  in  the  secondary  circuit,  and  a  c.  E.  M.  F.  is  set 

up  in  the  primary  circuit  under  the  influence  of  the  cur- 


I 


RA 

EQ. -RESISTANCE  45  OHMS 


Site.  Engineer 


FIG.  99. 

Illustrating  Equivalent  Resistance,  Reactance  and  Impedances  of  Mutually  Inductive 

Circuits. 

rent  in  the  secondary  circuit.  Without,  however,  ana- 
lyzing the  direction  and  magnitude  of  these  E.  M.  F.'S,  it 
is  sufficient  to  modify  the  impedance  of  the  primary  cir- 
cuit in  order  to  determine  the  results  produced.  If 
j?a,  !£*•>  e/aj  represent  respectively  the  resistance,  reactance 
and  impedance  of  the  primary  circuit,  r^  &b,  and  «/b,  the 
corresponding  quantities  in  the  secondary  circuit  and 

0)  L 


then  fi^  has  to  be  increased  by  n*  r^  to  J?4  ;  and  K^  di- 


256 


minished  by  n2  Kb  to  K^  ;  when  the  impedance  J±  =  72  A 
+  7jTA,  is  the  equivalent  impedance  of  the  primary  circuit. 
Thus,  if  a  primary  circuit  of  20  ohms  resistance  and 
100  ohms  reactance  have  impressed  upon  its  terminals  a 
sinusoidal  E.  M.  r.  of  100  volts,  whose  angular  velocity 
is  1000  radians  -per  second,  and  is  linked  through  a  mutual 
inductance  of  0.05  henry,  with  a  secondary  circuit  of 
resistance  rb  of  50  ohms,  reactance  &b,  of  50  \  90°  ohms, 
and,  therefore,  an  impedance  of  70.7  \  45°  ohms,  as 

shown  in   Fig.    99,—  then  n  =    100°  X  °-05  =  0.707 

70.7 

and  n2  =  0.5,  so  that  the  primary  resistance  has  to  be 
increased  by  0.5  X  50  =  25  ohms,  and  the  secondary  re- 
actance diminished  by  0.5  X  —  50  =  —  25,  i.  e.,  increased 
by  25  ohms,  so  that  the  equivalent  resistance  7?A,  is  45 
ohms,  the  equivalent  reactance  7TA  125  /90°  ohms,  and 
the  equivalent  impedance  132.8  /70°  12'.  The  primary 


current  is,  therefore  132  8       Q°  12/  =  0.753   \  70°  12'. 


The  secondary  E.  M.  F.  is  expressed  by  —  j  to  L^  7A  = 

to  L    7A  \^W  =  50  \TJO°  X  0.753  \~70~°  12r  =  37.65 


\  160°   12;,    and   this    secondary    current    7b    will   be 
37.65  060^  m  ^ 

70.7  \  45° 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


[Copyright,  1894,  by  THH  ELECTRICAL  ENGINEER.] 
WEEKLY. 


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ADVANCED      GRADE. 

ALTBRN  ATTORN. 


259.  The  essential  difference  between  an  alternator 
and  a  continuous-current  generator  is  that  the  al- 
ternator has  to  supply  an  alternating  E.  M.  F.  of  definite 
frequency  and  of  definite  wave  character,  whereas  the 
continuous-current  generator  has  only  to  supply  a  con- 
stant E.  M.  F.  If  p,  be  the  number  of  poles,  or  the  num- 
ber of  magnetic  circuits  in  the  alternator  field,  and  if  /?, 
l>e  the  number  of  revolutions  made  by  the  armature  per 

second,  the  frequency  will  be  &  n  periods  per  second, 

except  in  the  case  of  some  inductor  alternators  whose 
frequency  is  p  n  ~.  Thus  a  bipolar  machine,  to  produce 
a  frequency  of  1.00  ~,  would  have  to  make  100  revolu- 
tions per  second,  or  0000  revolutions  per  minute,  a  speed 
only  attained  by  steam  turbines.  Consequently,  almost 
all  commercial  alternators  are  multipolar  machines,  some 
having  as  many  as  112  poles.  The  lower  the  frequency 
adopted  on  a  circuit,  the  smaller  the  number  of  poles,  or 
the  fewer  the  number  of  revolutions  per  minute. 

Published  by 

THE    ELECTRICAL  ENGINEER, 
203  Broadway,  New  York,  N.  Y. 

[Entered  as  second  class  matter  at  the  New  York,  N.  Y.,  Pott  Office,  June  14,  1804.] 


258 


260.  The  shape  of  the  wave  of  E.  M.  F.  produced  by 
an  alternator  depends  primarily  upon  the  rate 

from  instant  to  instant,  at  which  flux  is  linked  with  the 
armature-winding  during  revolution.  It  will,  therefore, 
vary  with  the  shape  of  the  poles  and  with  the  shape  of 
the  winding  on  the  armature. 

The  simplest  form  of  wave  that  can  be  produced  by 
an  alternator  is  a  sinusoidal  wave.  As  already  men- 
tioned, many  alternators  produce  a  close  approximation 
to  the  sinusoidal  wave  form,  but,  no  matter  how  far  the 
wave  may  deviate  from  a  strictly  sinusoidal  form,  it  may 
always  be  considered  as  a  combination  of  a  number  of 
sinusoidal  waves,  or,  in  other  words,  as  a  complex  sinu- 
soidal wave.  According  to  what  is  known  as  Fourier's 
theorem,  every  periodic  and  single-valued  wave  of  what- 
ever complexity,  may  be  resolved  into  a  combination  of 
a  single  fundamental  wave  or  simple  sinusoid,  having 
the  frequency  of  the  complex  wave,  and  a  number  of 
shorter  sinusoidal  waves  or  harmonics,  whose  frequen- 
cies are  all  some  integral  multiple  of  the  fundamental 
frequency. 

261.  The  first  harmonic  has  a  frequency  twice  that 
of  the  fundamental.     The  second  harmonic  three 

times,  and  the  nth  harmonic,  n-j-1  times  that  of  the  fun- 
damental. In  some  forms  of  waves  the  complexity  is  so 
great  as  to  necessitate  the  resolution  into  an  indefinitely 
great  number  of  harmonics  superposed  upon  the  funda- 
mental, while  for  practical  purposes,  waves  may  usually 
be  considered  as  simply  composed  of  a  fundamental 
together  with  the  superposition  of  the  second,  fourth  and 
sixth  harmonics,  since  beyond  the  sixth,  the  eifect  of 
higher  harmonics  becomes  practically  negligible. 


259 


Fig.  100,  represents  at  A,  a  fundamental  wave  of  the 
sinusoidal  type  ;  B,  its  first  harmonic  ;  c,  its  second ;  D, 
its  third,  and  E,  its  fourth.  Fig.  101  represents  at  s, 
a  fundamental  sinusoidal  E.  M.  F.  of  800  volts  amplitude, 
i.  e.,  565.6  volts  effective  and  100  ~;  at  P,  its  first  har- 
monic of  400  volts  amplitude,  and  at  Q,  its  second  har- 
monic of  500  volts  amplitude.  If  these  E.  M.  F.'S  were 


FUNDAMENTAL 


V  V 

vwww 


Elec.  Kngi 


FIG.  100. 


FIG.  101. 


independently  produced  by  three  separate  alternators, 
which  could  be  coupled  rigidly  together  on  the  same 
shaft,  then  when  alternators  P,  and  Q,  were  so  connected, 
starting  together  from  the  zero  in  the  same  direction,  the 
E.  M.  F.  which  would  be  produced  is  shown  in  Fig.  102. 
If  all  three  were  connected  together  the  resultant  wave 
type  of  E.  M.  F.  is  represented  in  Fig.  103. 


260 


262.  It  is  evident  from  an  inspection  of  Figs.  102  anci 
103,  that  no  ordinary  alternator  could  produce 
such  types  of  wave  as  are  there  represented,  because  the 
positive  waves  are  not  geometrical  inversions  of  the  neg- 
ative waves,  with  respect  to  the  zero  line.  Thus  the 
negative  wave  D  E  F  G  H,  should  continue  from  D,  to  the 
point  as  far  below  the  zero  line  as  A,  is  above  it,  in  order 
to  represent  the  symmetry  that  must  be  developed  in  an 
alternator  where  the  various  outlines  of  a  positive  wave 
are  repeated  in  due  succession  in  the  negative  wave,  with 
mere  alteration  of  direction.  The  discrepancy  is  due  to 


-Else.  Engineer 


FIG.  102. 


Elec.Engineer 

FIG.  103. 


the  introduction  of  the  first  harmonic.  It  can  be  shown, 
that  in  order  to  maintain  the  symmetry  referred  to,  only 
the  even  harmonics,  that  is,  second,  fourth,  sixth,  etc., 
can  be  present ;  that  is,  those  harmonics  whose  frequency 
is  an  odd  number  of  times  that  of  the  fundamental  fre- 
quency. Fig.  104  represents  the  combination  of  a  fun- 
damental sinusoidal  wave  of  E.  M.  F.  with  its  second 
harmonic  of  200  volts  amplitude  in  two  different  cases 
of  phase  relationship.  At  F  -f-  A,  the  fundamental  F, 
and  second  harmonic  A,  are  united,  while  at  F  -f-  B,  the 
same  fundamental  and  B,  are  united.  "It  is  evident, 


261 


therefore,  that  the  marked  presence  of  a  second  harmonic 
in  an  alternating-current  wave  may  produce  either  a  flat 
topped  or  a  peaked  form  of  wave,  according  to  the  phase 
of  the  harmonic,  relatively  to  the  fundamental. 

Any  alternating  E.  M.  r.  may,  therefore,  be  expressed 
by  the  formula, 

e   =  E\  sin  (cot  +  «i)  +  Ez  sin  (3  tot  +«3) 

sin  (5  tot  +  05)  +  •  •  •  •  volts 


FUNDAMENTAL 


-     HARMONIC 


FIG.  1C5. 


FIG.  104. 


where  e,  is  the  instantaneous  value  of  the  E.  M.  F.,  the 
frequency,  E^  E^  E5  the  amplitudes  of  the  fundamental 
and  the  second  and  fourth  harmonics,  and  a19  «3,  «5,  the 
respective  phase  angles.  If  it  be  required  to  eliminate 
the  phase  angles,  this  may  be  done  by  resolving  each 


262 


successive  wave  into  two  sinusoidal  components  in  quad- 
rature,  thus 
e  =  Et  sin  cot  +  E'  cos  cot  +  Eitl  sin  Scot  -f- 

E"  cos  3  cot  +  EV  sin  5  ^  -f  ^v  cos  5  w  tf,  -f- 

This  equation  is  one  expression  of  Fourier's  theorem. 
The  same  applies  to  any  alternating  current,  if  *',  and  /, 
be  substituted  for  e,  and  E,  respectively. 

263.  When  a  complex-harmonic  E.  M.  F.;  that  is,  an 
E.  M.  F.  distinctly  deviating  from  the  simple-sinu- 
soidal type,  sends  a  current  through  a  circuit  containing 
inductance,  the  reactance  of  the  circuit  to  the  harmonics 
will   be  greater  than  to  the  fundamental  E.  M.  F.,  and, 
therefore,   the    impedance  will  be  greater  to  the  har- 
monics. For  this  reason  the  components  of  harmonic  cur- 
rents are  weakened  relatively  to  the  fundamental,  and 
the  current  tends  to  approach  the  sinusoidal  form  more 
closely  than  the  E.  M.  F.     When,  however,  the  circuit  is 
linked  with  iron,  the  presence  of  hysteresis  will  usually 
introduce  a  greater  amount  of  distorsion  than  the  induct- 
ance can  compensate,  so  that  the  current  supplied  to  al- 
ternating   current    transformers,   particularly    on   light 
loads,  are  usually  much  distorted. 

264.  When  two  alternators  are  connected  in  series 
and  driven  by  independent  sources  of  power,  the 

armatures  tend  to  take  up  such  a  position  that  the  E.  M.  F. 
waves  of  one  are  in  the  opposite  direction  to  the  E.  M.  r. 
waves  of  the  other,  so  that  no  resultant  E.  M.  F.  is  de- 
veloped. For  this  reason,  when  alternators  have  to  be 
connected  together,  they  are  connected  in  parallel  in- 
stead of  in  series  unless  rigidly  connected  on  the  same 
shaft. 


263 


When  two  alternators  are  connected  in  parallel,  they 
must  necessarily  keep  step,  and  their  phase  difference 
must,  therefore,  be  constant,  within  certain  limits.  Sup- 
pose two  alternators,  of  1100  volts  effective  E.  M.  F.,  run- 
ning independently,  be  suddenly  connected  together 
at  a  time  when  their  phase  difference  is,  for  example,  as 
represented  in  Fig.  105.  The  E.  M.  F.  existing  in  the 
circuit  connecting  the  two  armatures,  whose  E.  M.  F.'S,  are 
represented  in  magnitude  and  phase  by  o  A,  and  o  B,  will, 
therefore,  be  represented  by  the  line  A  B,  and  this  E.  M.  F. 
tends  to  send  a  current  through  the  armature,  whose 
effect  \vill  be  to  accelerate  the  lagging  armature  and  re- 
tard the  leading  armature,  thus  bringing  the  machines 
into  phase.  On  the  other  hand,  by  armature  reaction, 
the  current  will  tend  to  produce  a  c.  M.  M.  F.  in  the  vari- 
ous magnetic  circuits,  tending  to  weaken  the  E.  M.  F.  of 
the  leading  machine.  The  machines,  will,  therefore,  rap- 
idly fall  into  step,  or  out  of  step,  according  to  which  of 
these  influences  preponderates.  The  smaller  the  phase 
difference  existing  at  the  time  of  interconnection,  the  lesser 
the  liability  of  derangement  in  operation.  The  lower 
the  frequency  and  the  smaller  the  armature  reaction,  the 
more  readily  the  interconnection  can  be  brought  about. 
If  this  connection  be  made  at  an  unfavorable  moment, 
the  current  in  the  armatures  may  reach  unduly  great 
strengths,  sufficient  to  blow  the  fuses,  and  the  mechani- 
cal strains  brought  to  bear  upon  the  machines  are  liable  to 
be  excessive.  For  this  reason  with  alternators  at  Ameri- 
can frequencies  in  electric  lighting,  i.  e.,  from  120  ~  to 
135  ~~  parallel  workings  has  not  come  into  use.  although 
in  Europe,  where  the  frequencies  are  from  40  ~~  to 
100  ~,  parallel  working  is  the  general  practice.  In- 


264 


struments  called  phase  detectors  are  frequently  employed 
to  ascertain  the  right  moment  at  which  to  throw  the 
switch  connecting  two  machines  in  parallel. 

SYLLABUS. 

Any  single-valued,  periodic  function  may  be  analyzed 
into  a  sinusoidal  wave,  of  the  frequency  of  the  function, 
and  a  series  of  superposed  harmonics. 

The  n\h  harmonic  has  a  frequency  of  n-\-\.  times  that 
of  the  fundamental. 

A  complex  E.  M.  F.  acting  upon  a  circuit  of  con- 
siderable reactance  tends  to  generate  a  current  more 
nearly  sinusoidal  in  type. 

Alternators  connected  in  series,  unless  rigidly  con- 
nected together,  tend  to  annul  each  other's  E.  M.  F. 

Alternators,  when  suddenly  connected  in  parallel,  may 
either  fall  into  step,  or  short  circuit  one  another,  accord- 
ing to  the  nature  of  the  machines,  the  armature  reaction, 
frequency,  and  the  phase  difference  between  them. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


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AND 
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ADVANCED      CRADE. 

ALTKRNATORS. 


265.  A  multiphase  alternator,  or  multiphaser,  as  distin- 
guished from  a  uniphase  alternator,  or  uniphaser, 

is  a  machine  which  generates  two  or  more  alternating 
currents  in  definite  phase  relationship  with  each  other. 
Multiphase  alternators  are  diphase  when  they  produce 
two  separate  alternating  E.  M.  F.'S  in  quadrature,  or  sepa- 
rated by  a  quarter  cycle,  and  triphase  when  they  pro- 
duce three  separate  alternating  E.  M.  F.'S  separated  by 
one-third  of  a  cycle.  Multiphase  generators  are  only 
required  for  the  purpose  of  operating  alternating  cur- 
rent motors,  which  can  start  from  rest  at  full  torque  ; 
that  is,  induction  motors. 

266.  Diphase   generators  employ   on   the   armature 
two  sets  of  coils  or  windings  so  arranged  that  the 

E.  M.  F.'S  generated  in  them  shall  have  the  same  magnitude, 
frequency  and  wave  type,  but  shall  differ  in  phase  by 
90°,  or  a  quarter  cycle,  so  that  the  diagram  representing 
such  effective  E.  M.  F.'S  will  be  shown  in  Fig.  106.  The 

Published  by 

THE  ELECTRICAL  ENGINEER, 
303  Broadway,  New  York,  N.  Y. 

[Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  June  14,  1894.] 


266 


current  produced  by  these  two  E.  M.  F.'S  may  be  carried 
in  two  independent  circuits,  necessitating  four  wires  and 
four  collector  rings,  as  in  Fig.  107,  or  in  two  inter-con- 


n 


100  VOLT  8  ^    ^— XOJ ~\~\^  Jilec.£n<jineer 

Elec.Kngineer  LJ 

FIG.  106.  FIG.  107. 

Diagram  of  Diphase  E.  M.  F.'S.  Biphase  Connections,  Separate  Circuits. 

nected  circuits,1  with  one  common  return  requiring  three 
wires  and  three  collector  rings,  as  in  Fig.  108. 

The  E.  M.  F.  between  the  collector  rings  A  and  o,  will 
in  the  latter  case,  be  the  same  as  between  B  and  o,  while 
the  E.  M.  F.  between  the  jings  A  and  B,  will  be  equal  to 
the  length  of  the  line  B  A,  joining  the  extremities  of  o  B 
and  o  A,  Fig.  106;  or  supposing  o  A  and  o  B,  to  be  each 
equal  to  <?,  the  E.  M.  F.,  B  A  will  be  e  V%.  When  the  third 
wire  is  employed  as  a  common  return  circuit,  as  for  ex- 
ample, wire  (2)  in  Fig.  108,  the  current  it  carries  will  be 


Elec.Enyineer 


FIG.  108. 

Diphase  Connections,  Interconnected  Circuits. 

the  sum  of  the  two  currents  in  circuits  x  and  Y,  which,  be- 
ing in  quadrature,  will  be  represented  as  in  Fig.  109,  and 
will  be  i  V%,  where  *,  is  the  current  strength  in  each  circuit. 


267 


The  cross-section  of  wire  (2)  will,  therefore,  have  to  be 
4:1  per  cent,  greater  than  that  of  either  of  the  two  other 
wires  in  order  to  have  the  same  drop  of  pressure  when 
the  two  circuits  x  and  Y,  are  similar  in  all  respects. 

267.     Triphase  generators  are  wound  in  two  ways ;  that 

is,  the  star  winding  and  the  triangular  winding, 

as  shown  in  Figs.  110  and  111.     A  combination  of  the 

two  has  also  been  introduced  as  shown  in  Fig.   112,  but 

owing  to  its  greater  complication  it  is  seldom  employed. 

The  winding  of  a  triphase  alternator  may,  therefore, 
be  effected  by  employing  three  separate  sets  of  coils, 


FIG.  109. 

I  Hagram  of  sum  of  two  equal 
Diphase  Currents. 


FIG.  110. 

Star  Triphase  Winding. 


FIG.  111. 

Triangle  Triphase 
Winding. 

each  generating  an  E.  M.  F.  of  equal  magnitude,  frequency 
and  wave  type,  but  differing  in  phase  by  |  cycle.  Or, 
they  may  be  made  to  differ  by  J  cycle,  so  far  as  re- 
gards their  production  in  the  armature,  and,  by  reversing 
the  intermediate  E.  M.  r.  relatively  to  the  external  circuit, 
the  spacing  is  converted  into  J  cycle,  as  shown  in  Fig. 
113,  where  OA,  OB  and  oc,  represent  three  equal  E.  M.  F.'S 
of  ^  cycle  angular  displacement.  The  E.  M.  F.  of  o  B, 
being  reversed,  with  respect  to  the  external  circuit,  be- 
comes o  B',  when  o  A,  o  c,  and  o  B',  are  three  triphase 
E.  M.  F.'S  displaced  by  ^  cycle. 


268 


(The  E.  M.F.  of  a  tri  phase  alternator;  that  is,  a  triphaser, 
is  not  measured  from  the  common  connection  o,  to  the 
terminals  A  B,  or  o,  but  between  any  pair  of  terminals 
A  B,  B  c  or  c  A.  The  E.  M.  F.  so  measured  will  be  repre- 
sented by  the  lengths  of  the  line  A  B,  B  c  or  c  A,  and  if 
the  effective  E.  M.  F.  in  each  branch  o  A,  o  B  or  o  c,  be  de- 
noted by  £,  the  effective  E.  M.  F.  between  any  pair  of 
terminals  will  be  e  V$. 


Elec.  Engineer 


FIG.  112.  FIG,  113.  FIG.  114. 

Combination  Triphase        Diagram  representing  the  trans-        Triphase  E.  M.  E.  Dia- 
Winding.  formation  of  %  cycle  E.  M.F.  's  into    gram. 

External  Triphase  E.  M.  K.'S. 

268.  A  triangular  winding  may  be  obtained  in  a  bi- 
polar machine  by  tapping  the  armature  at  three 
points  120°  apart,  as  shown  in  Fig.  114,  when  a  tri  phase 
E.  M.  F.,  not  usually  sinusoidal,  will  be  generated. 

In  multipolar  triphase  machines,  the  armature  is  wound 
with  three  sets  of  coils  which  are  subsequently  connected 
either  in  series,  that  is,  triangularly ;  or  in  parallel ;  that 
is,  star-connected.  If  e  be  the  effective  E.  M.  F.  of  each 
winding,  the  E.  M.  F.  of  a  triangularly  connected  ma- 
chine, between  any  pair  of  terminals,  will  be  0,  and  in  a 
star  connected  machine  the  E.  M.  F.  between  any  pair  of 


269 

terminals,  will  be  e  4/3.  The  out-put  in  both  cases  will 
be  the  same  ;  for,  if  a  triangular  triphaser  have  a  load 
represented  by  a  resistance  r,  connected  to  each  pair  of 
terminals  as  shown  in  Fig.  Ill,  the  current  in  each  cir- 

p 

cuit  will  have  the  numerical  strength  -  =  i.  amperes  ;  e, 

r 

being  the  pressure  at  machine  terminals,  so  that  the 
output  of  the  machine  will  be  3  e  i  watts.  If,  however, 
a  star-triphaser  has  a  resistance  R  =  3  r,  connected  as  a 
load  to  each  pair  of  terminals,  the  current  *,  in  R,  will  be 


1.732  e  \30 


\  30 


3  r  Sr  1.T32 

e         e  /60C 


similarly,  the  current  in  R     will  be  *      = 

6  r 

_  i  /30° 
—     -——•  .    The  current  in  the  winding  O  A,  will  be  the 

J..7o<a 


The  external  activity  of  this  winding  will,  therefore, 
be  e  i  watts,  and  the  total  external  activity  of  the  ma- 
chine 3  e  i  watts,  as  before.  In  order  that  the  star-tri- 
phaser shall  have  the  same  activity,  as  the  triangular-tri- 
phaser,  its  resistance  must  be  3  r,  on  each  circuit  ;  that 
is,  its  load  must  be  J-  of  the  load  on  the  triangular  tri- 
phaser. The  E.  M.  F.  of  the  star  triphaser  is,  therefore, 
y8  times  the  E.  M.  F.  of  a  triangular  triphaser  of  the  same 
winding,  but  will  carry  -J  of  the  current  strength  in 
the  external  circuits  that  a  triangular  triphaser  will  sus- 
tain. It  is,  therefore,  necessary  to  reduce  the  number 
of  turns  in  a  star-triphaser  by  about  43  per  cent,  in  order 
to  produce  the  same  E.  M.  F.  at  terminals  as  a  triangular 


triphaser,  and  to  utilize  the  winding  space  so  gained  for 
an  increased  conductivity,  in  the  proportion  of  1.732. 
The  E.  M.  F.  at  the  terminals  of  both  machines  will  then 
be  the  same,  and  the  drops  in  each  machine  the  same. 

269.     Fig.  115  represents  a  star-triphaser  ABC,  con- 
nected to  the  star  load  A',  B',  c',  the  load  of  whish 
may  consist  either  of  loaded  transformers,  of  diphase 


,EUC.£n<ri«««r 


FIG.  115. 

Diagram  and  Analysis  of  Tnphase  Circuit. 


motors,  of  lamps,  etc.  It  is  evident  that  the  middle 
points  o  and  o',  are,  by  symmetry,  always  at  zero  poten- 
tial when  the  system  is  perfectly  insulated,  so  that  the 
ground  plates  G,  G,  may  be  connected  to  this  point  at  each 
end  of  the  line  without  altering  the  distribution  of  cur- 


371 

rents  and  potentials,  and,  therefore,  without  carrying  any 
current  through  the  ground  ;  for,  if  the  loads  on  the 
three  circuits  be  equally  balanced,  the  current  in  o  A,  will 
be  the  vector  sum  of  the  currents  in  o  B  and  o  c.  For 
purposes  of  transmission,  therefore,  the  circuits  may- 
be regarded  as  constituting  three  separate  uniphase  cir- 
cuits o  A"  A"'  o,  o  B"  B  o,  and  o  c"  c'"  o,  each  employ- 
ing a  ground  return  circuit  of  zero  resistance  ;  so  that  a 
triphaser  supplying  1000  volts  at  its  terminals  is  equiva- 
lent, in  regard  to  pressure  of  delivery  and  economy  in 
conductor,  to  a  uniphaser  at  577.4  volts  pressure  with 


V  G 

El: 

FIG.  116. 

Monocyclic  E.  M.  F.  Diagram. 

ground  return,  or,  to  a  uniphaser  of  1155  volts  employing 
a  simple  return  circuit. 

270.  A  recent  combination  of  uniphase  and  triphase 
systems  is  called  the  wonocyclic  system. 

A  monocyclic  alternator  is  wound  with  two  circuits, 
one  of  which  is  the  principal  circuit  and  has  the  princi- 
pal E.  M.  F.,  o  A,  Fig.  116,  for  uniphase  transmission, 
while  the  second  circuit  has  a  smaller  wire  of  fewer 
turns  with  an  E.  M.  F.,  B  c,  in  quadrature  with  A  B,  and 
about  J  of  the  E.  M.  F.,  o  A.  The  second  winding  is  con- 
nected to  the  middle  of  the  main  winding  as  shown.  The 
terminals  o,  A,  are  connected  to  the  incandescent  lighting 
mains,  and  the  E.  M.  F.  between  these  terminals  will  be 


272 


simply  Uniphase.  Where,  however,  induction  motors 
are  required  to  be  operated  with  full  starting  torque,  a 
third  or  power  wire  connected  to  the  terminal  B,  is  brought 
into  connection  with  the  motor  through  two  transformers 
o  c  and  c  A,  connected,  as  shown  in  Fig.  117.  The 


SECONDARY 
Q'l  100  VOLTS 


nfflflffltfRfflfflSW^ 

\r\         1154  Tr         119*  I™ 

|°        PRIMARY  °         PRIMARY 


Eltc.Engineer 

FIG.  117. 

Monocyclic  Triphase  Transformer 
Connections. 


Combination  of  Secondary  Monocyclic 
E.  M.  F.  into  Triphase  System. 


E.  M.  F.'S,  suitably  reduced  by  transformers,  are  o'  c'  and 
c'  A',  Fig.  118,  differing  in  phase  by  60°.  By  reversing 
the  secondary  connections  of  the  E.  M.  F.,  c'  A',  the 
E.M.  F.'S  developed  are  o-  c',  c'  A",  and  their  sum  o'  A", 
which  are  three  triphase  E.  M.  F.'S.  and  which  may  be 
connected  to  the  terminals  of  a  triphase  motor. 

Laboratory  of  Houston  &  Kermelly, 
Philadelphia. 


[Copyright,  1894,  by  THB  ELECTRICAL  ENGINEER.! 
WEEKLY. 


No.  35.  FEBKUAKY  9,  1895. 

Electrical   Engineering   Leaflets, 


Prof.  E.  J.  Houston,  Ph.  D. 

AND 

A.  E.  Kennelly,  F.  R.  A.  S. 


ADVANCED      GRADE. 

Alternating  Current  Transformers, 


271.  An  alternating-current  transformer-  is  a  device 
for  inducing  an  E.  M.  F.  in  a  secondary  circuit  mag- 
netically linked  with  a  primary  circuit,  under  the  influ- 
ence of  an  alternating  current  in  the  primary. 

A  transformer  enables  a  powerful  alternating  current 
to  he  developed  in  a  local  consumption  circuit  without 
the  necessity  of  conveying  the  current  over  a  long  dis- 
tance, thus  avoiding  either  the  heavy  loss  of  energy,  or 
the  heavy  expenditure  in  conductors,  which  would  other- 
wise he  necessary.  The  energy  may  be  transmitted  over 
the  main  circuit  at  high  pressure  with  a  small  current 
strength,  and  is  transformed  locally  to  a  lower  pressure 
and  correspondingly  increased  current  strength.  Such  a 
transformer  is  called  a  step-down  transformer.  On  the 
other  hand,  a  transformer  employed  to  raise  the  pressure 
and  diminish  the  current,  is  called  a  step-up  transformer. 
The  ratio  of  transformation  is  the  ratio  of  the  effective 
E.  M.  F.  at  secondarv  terminals  to  the  effective  E,  M.  F.  at 


Published  by 

THE  ELECTRICAL  ENGINEER, 
903  Broadway,  New  York,  N.  Y. 

\ Entered  as  second-class  matter  at  the  New  York,  N.  Y.,  Post  Office,  Juoe  14, 1894.] 


primary  terminals  on  open  circuit.  The  ratio  of  trans- 
formation in  a  step-down  transformer  is,  therefore,  always 
less  than  unity,  and  in  a  step-up  transformer  always 
greater  than  unity.  The  transformers  ordinarily  em- 
ployed in  electric  incandescent  lighting  usually  step- 
down,  from  a  pressure  of  1000  or  2000  volts  in  the  prim- 
ary mains,  to  50  or  100  volts  in  consumption  circuits,  and, 
therefore,  have  a  ratio  of  transformation  of  from  T^  to  ^ 
If  a  ring  of  iron  wire  c  c  c,  Fig.  119,  be  wrapped  with 
a  primary  coil  p,  of  JV  turns,  and  connected  to  an  alter- 
nating effective  voltage  £]  the  c.  E.  M.  F.  of  self-induc- 
tion added  geometrically  to  the  udrop"  in  the  coil  must 
be  equal  to  E.  Since  the  drop  in  the  primary  coil  of  a 
small  transformer  at  full  load  would  not  exceed  two  per 
cent.,  while  in  a  large  transformer  it  would  be  less  than 
one  per  cent.,  we  may  practically  ignore  the  drop,  and 
consider  that  the  c.  E.  M.  F.  produced  by  the  transformer 
must  be  equal  and  opposite  to  this  impressed  E.  M.  F. 
Consequently,  whatever  be  the  wave  form  of  the  im- 
pressed E.  M.  F.,  the  wave  form  of  the  c.  E.  M.  F.  devel- 
oped must  be  the  same.  The  flux  through  the  magnetic 
circuit  of  the  primary  coil  must,  therefore,  be  such  that 
the  rate  of  change  in  the  flux-linkage,  shall  at  every  instant 
be  equal  to  the  impressed  E.  M.  F.,  in  c.  G.  s.  units.  Ex- 
pressed in  symbols,  if  <0,  considered  as4  a  variable  depend- 
ent upon  time,  be  the  flux  linkage  in  the  primary  cir- 
cuit, expressed  in  weber-turns ;  then  neglecting  drop, 

SSt  =  e',  where  <?',  is  the  instantaneous  value  of  the  ef- 
dt 

fective  E.  M.  F.  E,  expressed  in  c.  <;.  s.  units. 

The  current-strength,  which  will  pass  through  the  pri- 
mary coil  at  each  instant,  is  such  that  the  M.  M.  F.  it  de- 
velops in  the  coil  shall  maintain  the  flux  linkage  <#, 


275 


As  a  simple  example,  suppose  a  primary  coil  of  500 
turns,  and  2  ohms  resistance,  to  be  wound  on  a  magnetic 
circuit  of  0.002  oersted  reluctance,  and  connected  to  a 
sinusoidal  E.  M.  F.  of  1000  volts  effective,  with  800  radi- 
ans per  second  angular  velocity.  Assuming  the  absence 
of  hysteresis  and  eddy  currents,  and  that  all  the  flux 
passes  through  all  the  turns,  the  effective  flux  must  be 
250,000  webers,  for  the  flux-linkage  will  be  250,000  X 
500  =  125,000,000  weber  turns,  and  the  time  variation 
of  this  will  be  800  X  125,000,000  =  1011  c.  o.  s.  units 
of  E.  M.  F.  =  1000  volts.  The  effective  M.  M.  F.  required 
to  produce  this  flux  will  be  250,000  X  0.002  =  500 
gilberts  =  400  ampere-turns  approximately,  or  0.8  am- 
pere effective  through  the  coil.  This  is  called  the  excit- 
ing or  magnetizing  current. 

Under  all  conditions  of  load  in  a  transformer,  the  re- 
sultant M.  M.  F.  remains  constant,  when  the  drop  in  the 
primary  coil  may  be  neglected. 

272.     If  now  the  secondary  coil  s,  of  n  turns,  Fig.  119, 
be  wound  on  the  ring,  no  change  will  take  place 
in  the  primary  circuit,  so  long  as  the  secondary  coil  is 
open,  but  the  flux  pulsating  through  the  magnetic  cir- 
cuit and  the  secondary  coil,  will  set  up  an  E.  M.  F.  of  e  = 

v 
^^TT  ,  effective  volts  in  the  latter. 

When  the  secondary  coil  has  its  circuit  closed  through 

a  total  impedance  </,  a  current  of  i  amperes  =  -  will 

J 

pass  through  the  secondary  circuit,  and  a  M.  M.  F.  of  n  i 
effective  ampere-turns  will  then  be  imposed  upon  the 
magnetic  circuit.  If  the  secondary  load  be  non-inductive, 
say,  a  series  of  incandescent  lamps,  and  if  there  existed  no 


276 


leakage  flux  in  the  transformer  magnetic  circuit,  this 
M.  M.  F.  will  be  in  step  with  the  induced  secondary  E.  M.  r.; 
that  is  to  say,  it  will  be  in  step  with  the  primary  c.  E.  M.  F. 
and,  neglecting  primary  drop,  it  will  be  in  opposition  to 
the  impressed  E.  M.  F.  It  will  therefore  be  opposed  to 
the  M.  M.  F.  in  the  primary  circuit.  The  resultant  will 
be  a  M.  M.  F.  at  a  phase  intermediate  between  them.  In 
order  to  maintain  the  resultant  M.  M.  F.  at  the  magnitude 
and  phase  of  the  M.  M.  F.  of  excitation,  a  greater  current 
strength  will  enter  the  primary  coil. 

Consequently,  as  load  is  added  to  the  secondary  cir- 
cuit, the  primary  current  is  compelled  to  vary  both  in 
magnitude  and  phase,  so  as  to  maintain  the  fixed  M.  M.  F. 
of  excitation  as  a  resultant.  The  result  is  a  stronger  pri- 
mary current,  a  greater  primary  power  factor,  and  a 
greater  primary  activity.  An  automatic  adjustment  is 
thus  maintained  in  the  primary  c.  E.  M.  F.,  whereby  elec- 
trical energy  is  transferred  from  the  primary  to  the  sec- 
ondary circuit. 

The  foregoing  operations  might  be  readily  observed 
and  computed  in  any  transformer,  if  they  were  not  con- 
siderably complicated  both  by  hysteresis  and  leakage. 

Owing  to  hysteresis,  the  M.  M.  F.  needed  to  establish 
the  primary  c.  E.  M.  F.  is  not  of  the  same  wave  type  as 
the  latter,  and  is  different  in  the  ascending  and  descend- 
ing branches  of  each  wave  of  flux,  as  is  readily  observed 
from  an  inspection  of  Fig.  59.  The  simplest  existing 
means  of  predetermining  the  current  wave,  is  by  the 
graphical  application  of  Fig.  59  to  the  c.  E.  M.  F.  wave 
required,  so  as  to  determine  the  primary  M.  M.  F.  and  cur- 
rent strength  at  different  points  in  the  cycle.  Energy  is 
expended  in  the  primary  circuit  and  absorbed  in  the 


.an 


core  of  the  transformer  hysteretically,  as  explained  in 
Sec.  151. 

The  effect  of  leakage  is  to  unduly  increase  the  drop  at 
secondary  terminals  under  load.  If  there  were  no  leak- 
age, that  is,  if  all  the  flux  passed  through  each .  primary 
and  secondary  turn,  the  secondary  coil  would  act  as 
through  devoid  of  inductance  and  possessing  only  ohrnic 
resistance,  its  inductive  reaction  being  entirely  expended 
against  the  primary  circuit ;  but  if  some  of  its  flux  es- 
capes the  primary  coil,  that  portion  developes  a  c.  E.  M.  F. 
of  self-induction  in  the  secondary  coil,  and  an  apparent 
inductance  is  added  to  the  secondary  circuit  within  the 
transformer,  increasing  the  drop  at  load.  In  practice, 
theie  is  always  some  leakage  in  a  transformer,  and  the 
secondary  drop  due  to  leakage  is  frequently  as  great  as 
the  drop  due  to  the  ohmic  resistance  of  both  coils.  One 
of  the  principal  objects  in  the  design  of  a  transformer  is 
the  reduction  of  magnetic  leakage  to  a  minimum ;  for, 
although  the  presence  of  leakage  does  not  give  rise  to 
waste  of  energy,  yet  it  produces  a  drop  in  pressure  which 
unduly  limits  the  output  of  the  apparatus  for  incandes- 
cent lighting. 

When  the  load  in  the  secondary  circuit  is  non-induc- 
tive, the  wave  form  of  secondary  current  will  be  very 
nearly  the  same  as  the  wave  type  of  secondary  E.  M.  F., 
and  therefore  of  impressed  E.  M.  F.  When  the  secondary 
load  is  inductive,  the  secondary  current  and  M.  M.  F.  lag 
behind  the  secondary  E.  M.  F.  .  This  necessitates  a  greater 
primary  M.  M.  F.  and  current  to  maintain  the  resultant 
M.  M.  F.  of  excitation,  and  not  only  is  the  primary  current 
strength  greater,  but  it  is  forced  into  more  nearly  com- 
plete opposition  with  the  secondary  current.  The  former 


effect  increases  the  ohmic  drop  and  the  latter  effect  in- 
creases the  leakage  drop,  since  the  two  opposing  M.  M.  F.'S 
produce  a  greater  magnetic  difference  of  potential  be- 
tween the  opposite  surfaces  of  the  magnetic  circuit  F  F, 
Fig.  119. 


FIG.  119. 


273.     Let  o  E,  Fig.  120  c,  represent  the  effective  c.  E. 
M.  F.  in  the  primary  circuit  of  a   transformer  of 
say  1000  volts,  and  o  0,  the  effective  E.  M.  F.  in  the  sec- 
ondary circuit,  in  step  with  o  E.     When  the  secondary 


FIG.  120. 

circuit  is  open,  let  o  M,  400  /90°,  be  the  effective  M.  M.  F. 
in  gilberts  or  ampere-turns  required  to  maintain  the 
c.  E.  M.  F.,  o  c ;  then  the  primary  current  must  be  in  phase 
with  o  M.  JSTow  suppose  a  non-inductive  load  connected 


2T9 

to  the  secondary  circuit.  The  E.  M.  F.,  o  e,  will  send  a 
current  through  this  circuit  lagging  in  phase  very  little 
behind  o  «,  and  the  M.  M.  F.  of  this  current  will  be  o  w2, 
say  400  \~~5^.  I"  order  to  maintain  the  resultant  M.  M.  F. 
o  M,  the  primary  M.  M.  F.  must  assume  the  position  o  w, 
or  approximately  000  /H0°  and  thus  approach  in 
phase  the  impressed  E.  M.  F.,  which  will  be  equal  but  op- 
posite tO  O  E. 

If  now,  owing  to  magnetic  leakage  in  the  transformer, 
inductance  appears  in  the  secondary  coil,  the  second- 
ary current  and  M.  M.  F.  may  lag  15°,  as  shown  at  A, 


FIG.  121. 

and  the  primary  M.  M.  F.,  (o  M  -  -  o  />ia),  will  become 
approximately  625  /125°.  Again,  if  the  same  load  in 
watts  be  applied  inductively  to  the  transformer,  as,  for 
example,  an  alternating-current  motor,  the  power  factor 
of  the  secondary  circuit  will  be  reduced,  and  a  greater 
current  strength  will  be  required,  which  will  lag  con- 
sid,erably  and  the  M.  M.  F.  may  become,  as  at  B,  770  \  60°. 
The  primary  component  will  be  increased  to  approxi- 
mately 1100  /2<>°,  and  the  components  will  be  nearly  in 
opposition. 


280 


The  effect  of  this  opposition  in  M.  M.  F.'S  upon  the  leak- 
age through  both  coils  is  illustrated  in  Fig.  121.  If  om2 
and  6  m,  are  in  quadrature,  each  M.  M.  F.  is  at  its  maxi- 
mum when  its  neighbor  is  zero,  and  when  as  at  A,  rn  is 
at  its  maximum,  //i2,  is  absent,  and  the  flux  tli rough  the 
reluctance  R3,  of  the  leakage  path  will  be  only  that  due 
to  the  magnetic  drop  in  the  reluctance  R2,  of  the  iron  oc- 
cupied by  the  secondary  coil.  Similarly  when  m%,  is  at 
its  maximum  the  flux  through  R3,  is  that  due  to  the  drop 
in  KJ.  When,  however,  the  M.  M.  F.'S  are  forced  into  op- 
position, the  leakage  flux  from  each  through  K3,  is  in- 
creased. 

274.  The  power  factor  of  transformers  varies  not  only 
with  their  load,  but  also  with  the  nature  of  their 
load,  for,  when  the  secondary  circuit  is  loaded  inductively, 
the  current  in  the  secondary  circuit  lags  considerably  be- 
hind the  impressed  secondary  E.  M.  F.  Consequently  the 
c.  M.  M.  F.  is  brought  more  nearly  in  opposition  to  the 
primary  M.  M.  F.  The  drop  in  each  circuit  is,  therefore, 
increased  as  will  be  evident  from  an  inspection  of  Figs. 
120  and  121.  Large  transformers,  whose  power  factor 
may  be  0.995  at  full  non-inductive  load,  with  a  full  load 
drop  at  secondary  terminals  of  1  per  cent.,  may  have  a 
power  factor  of  0.90  with  an  inductive  load,  and  have 
their  full  load  drop  at  the  same  time  increased  to  4  per 
cent.  On  the  other  hand  a  condenser  connected  to 
secondary  terminals  tends  to  diminish  the  secondary  drop 
and  increase  the  power  factor. 

Laboratory  of  Houston  &  Kennelly, 
Philadelphia. 


INDKX. 


Activity,  Definition  of 7 

Activity  in  Carbon  Voltaic 

Arc 217,  218 

Admittance     249 

Aero-Ferric  Magnetic  Cir- 
cuit, Calculation  of. . .  109,  no 

Alloys 26 

All-Night  Arc  Lamps 224 

Alternating-Current     Arc 

Circuits 228,  229 

Alternating  Current,  Defi- 
nition of 233 

Alternating-Current   Arc, 
Distribution    of    Light 

from 228,  229 

Alternating  Current,  Mean 

or  Average  Strength  of. .     46 
Alternating-Current  Trans- 
former  273  to  280 

Alternating-Current  Trans- 
former,AutomaticAdjust- 

mentsof 275,  276 

Alternating-Current  Trans- 
former. Definition  of 273 

Alternating-Current  Trans- 
former,  Hysteretic  Loss 

in 276,  277 

Alternating-Current  Trans- 
former, Power-Factor  of.  280 
Alternating  Currents  233  to  256 
Alternating  E.  M.  F.,  Defini- 
tion of 233 


Alternating    or    Pulsatory 
Current ,    Determination 

of  Strength  of 46 

Alternation,  Definition  of..  234 
Alternator  and  Continuous 
Current    Generator,    Es- 
sential   Difference    b  e  - 

tween 257 

Alternator,  Diphase 265 

Alternator,  Uniphase 265 

Alternators 257  to  272 

Alternators,  Connection  of 

in  parallel 263 

Alternators,  Definition  of. .  238 
Alternators,  Multiphase....  265 

Ampere,  Definition  of 42 

Ampere-Hour,  Commercial 

Unit  of  Electric  Quantity    45 
Arc  Carbons ,  Consumption 

of 223 

Arc,  Counter-Electromotive 

Force  of 217 

Arc  Lamps,  All-night 224 

Arc  Lamp,  Ordinary,  Activ- 
ity of 7 

Arc    Lamps,    Alternating- 
Current  Circuit 228,  229 

Arc  Lamps,  Double-Carbon  224 
Arc  Light  Carbon,  Positive 
Crater  in 218 


282 


INDEX. 


Arc   Light    Circuits,    Con- 
tinuous,   Distribution    of 

Potential  in 226 

Arc  Light  Dynamos 225 

Arc  Light  Globes 231 

Arc  Light  Projectors  . .  229, 

230,  231 

Arc-Lights,  Mean  Horizon- 
tal Intensity  of 221 

Arc  Lights,  Mean  Spherical 

Candle-power  of 221 

Arc  Lighting 216  to  232 

Armature  of  Dynamo  and 
Motor,  Circumstances  Af- 
fecting Direction  of  Rota- 
tion of l87,  188 

Armature  Reaction i5o 

Armatures,    Toothed  Core 

of  Dynamos I52 

Attractive  Electromagnets, 

Definition  of II3 

Attractive  Force  of  Electro- 
magnets, Calculation  of 

114.  115,  116 

Balances,  Resistance,  Vari- 
ous Forms  of 28,  29 

Balance,  Wheatstone's.. 28,  29 
Battery,  Voltaic,  Efficiency 

of 7i 

Begohm,  Definition  of r8 

Bichromate  Voltaic  Cell .  84,  85 

Bicrohm,  Definition  of 18 

Bridge  Boxes,    Various 

Forms  of 28,  39 

Bridge,  Wheatstone's. . .  28,  29 
Brushes  of  Dynamo,  Lead 

of- M 149 


Brushes, Shifting  of  on  Com- 
mutator f  orVaryingSpeed 
of  Continuous  Current 
Motor 177>  I78 

C.  E.  M.  F.  of  Polarization. .     81 
c.  G.  s.,  Practical,    Unit  of 

E.  M.  F n 

c.  G.  s   Units 4,       5 

c.  G.  s.  Unit  of  Force 5 

c.  G.  s.  Unit  of  Quantity. ..     u 
Cable,  Insulation  Resi- 
stance of 35)     36 

Candle-Foot 206 

Candle-Power  of  Arc  Lights, 

Mean  Spherical 221 

Candle-Power  of  Incandes- 
cent Lamp,  Methods  Pro- 
posed for  Regulating, 2 1 2,  213 

Candle,  Standard 205 

Capability,     Electrical ,    of 

Voltaic  Cell 69,     7o 

Carbon  Voltaic  Arc,  Ac- 
tivity in 2i7,  218 

Carbons,  Cored 228 

Carbons,  Electro-plated 223 

Carcel  Lamp 205 

Carcel-Metre  2o6 

Carrying  Capacity  of  Con- 
ductors   45 

Cell,    Voltaic,  Bichromate, 

82,     83 

Cell,  Voltaic,  Clark  Standard    88 
'ell,    Voltaic,     Edison-La- 

lande 87,     88 

•ell,  Voltaic,  Electrical 

Capability  of 69,     7o 

Cell,  Voltaic,  Fuller  ....  86,     87 

lell,  Voltaic,  Gravity. . .  84,     85 

Cell,  Voltaic,  Grenet 82,    83 


INDEX. 


Cell,  Voltaic,  Leclanche...     85 
Cell,  Voltaic,  Partz   Gravi- 
ty  85,     86 

Cell,  Voltaic,  Poggendorff, 

82,     83 

Cell,  Voltaic,  Silver  Chlor- 
ide  87,     88 

Cell,  Voltaic,  Smee 82 

Centimetre-G  r  a  m  m  e  -  Se- 
cond Unit  of  Activity. ...       7 
Central  Lighting  Stations, 
Maximum  Lighting  Load 

of 212 

Central  Lighting  Stations, 
Minimum  Lighting  Load 

of 212 

Charge,  Electric,  and  Ether 
Strains,  Relation  between      2 

Charge,  Negative 2 

Charge,  Positive 2 

Circuit,  Drop  in 50 

Circuit,  Electric,  Definition 

of 57 

Circuit,  Ferric  Magnetic. .       93 

Circuit  Impedance 244 

Circuit,  Multiple-Series 60 

Circuit,  Reactance   244 

Circuit,  Resonant 248 

Circuits,  Conducting,  Clas- 
sification of 57 

Circuits,  Magnetic 92 

Circular  Type  of  E.  M.  F.  or 

Current 235 

Clark  Standard  Cell 15 

Clark  Standard  Cell,   Tem- 
perature Coefficient  of . . .     16 
Clark  Standard  Voltaic  Cell     88 
Coefficient  of  Reduction 
from   Capability  to  Out- 
put...  131,  132 


Coils,  Compensating 160 

Combin  ation     Triphase 

Winding 268 

Compensating  Coils,  of  Dy- 
namo    160 

Complex-Sinusoidal  Wave.  258 
Conductance,  Definition  of  25 
Conductances,  Formula  for 

Calculating 25 

Conducting  Circuits,  Classi- 
fication of 57 

Conductivity.  Definition  of    25 
Conductivity,  Magnetic. ...     95 
Conductor,  Electric,  Dissi- 
pation of  Heat  by 196 

Conductor,    Electric,  Tem- 
perature Elevation  of 198 

Conductors,  Carrying  Capa- 
city of 45 

Conductors,  Safe    Current 

Density  in 45 

Continuous-Current   Dyna- 
mo, Reversibility  of 170 

Cooling  of  Wire,  Effect  of 

Covering  on 198,  199 

Co-periodic  Simple-Harmo- 
nic E.  M.  F.'S,  Vector  Sum 

of 243 

Cored  Carbons 228 

Coulomb,  Definition  of . .  1 1 ,     42 

Couple,  Voltaic 66 

Counter- E  lectromotive 
Force,   Development    of, 
by  Continuous  Current . .     62 
Counter- Electro  motive 

Force  of  Arc 217 

Counter-  Electromotive 

Force  of  Arc,  Origin  of..  218 
Counter-Electromotive 
Force  of  Induction  . .  62 


284 


INDEX. 


Counter- E  lectromotive 

Force  of  Motor 170 

Counter-E  lectromotive 

Force  of  Polarization     .       62 
Counter-E  lectromotive 

Force,  Varieties  of 62 

Counter-E  lectromotive 

Force,  Virtual 62 

Crater  in  Positive  Arc  Light 

Carbon 218 

Current,   Alternating,    De- 
finition of 233 

Current,  Circular  Type  of 

Periodic-Alternating 235 

Current  Density 45 

Current,    Displacement, 

Probable  Nature  of 10 

Current,  Electric  ...  41  to    48 
Current,  Electric,  Does  Not 
Pass  Through  Conductor 

41,    42 

Current,  Periodic-Alternat- 
ing, Definition  of 233 

Current,  Sinusoidal 236 

Curve,  Sinusoidal 237 

Curve,  Simple-Harmonic  . .  237 

Curve,  Simple-Periodic 237 

Curves    of    Reluctivity    in 
Iron  and  Steel  in  Relation 

to  Flux  Density 107 

Cut-Out,  Film 213,  214 

Cycle,  Definition  of 234 

D.  E.  M.  F 170 

Daniell  Voltaic  Cell 84,     85 

Density  of  Current 45 

Density  of  Flux,  Definition 

of 90 

Depolarizer 8 1 


Derived  Circuit,  Applica- 
tion of  Ohm's  Law  to $2 

Detectors,  Phase 264 

Diagram,  Hysteretic 142 

Dielectric      Displacement , 

Current  in 2 

Dielectrics,  Maintenance  of 

Electric  Displacements  in      2 
Difference  of  Potential    ...     13 
Differential  Calculus,  Sim- 
ple Explanation  of 43 

Direct  Electromotive  Force 

of  Generator 1 70 

Diphase,  Alternator 265 

Diphase,  Connection  of  In- 
terconnected Circuits. .  . .  266 
Diphase  Connections,  Sep- 
arate Circuits 266 

Diphase  E.  M.  F.'S 266 

Displacement    Current, 

Probable  Nature  of 10 

Displacement  Flux,  Nature 

of 2 

Displacement  Strain.   ...9,     10 
Displacement,  Electric,  Na- 
ture of 2 

Double-Carbon  Arc  Lamps  224 
Double-Fluid  Cells,  Defini- 
tion of  82 

Drop  in  Circuit 50 

Dynamo  and  Motor,  Co- 
Generation  of  Electro- 
dynamic  and  Electro 

motive  Forces  in 169 

Dynamo,  Counter  Electro- 
dynamic  Force  of 1 70 

Dynamo-Electric  Machine, 

Armature  of 150,  151 

Dynamo-Electric  Machine, 
Classification  of  Losses  in  137 


INDEX. 


285 


Dynamo-Electric  Machine, 
Electrical  Losses  in. .  138,  139 

Dynamo-Electric  Machine, 
Lead  of  Brushes  of . .  .  .  149 

Dynamo-Electric  Machine, 
Limitations  to  Output  of, 
Classification  of 145 

Dynamo-Electric  Machine, 
Mechanical  Lossesin,  137,  138 

Dynamo-Electric  Machine, 
Principles  of  Design  of. . 

133,  134,  135 

Dynamo,  the 128,     152 

Dynamos  and  Motor,  Dif- 
ference of  Output  of .  181,  182 

Dyne,  Definition  of 5 

Dyne  Centimetre,  Defini- 
tion of . .  6 


E.  M.  F 9  to     16 

E.  M.  F.,  Alternating,  De- 
finition of 233 

E.  M.  F.,  Circular  Type  of 
Periodic-Alternating 235 

E.  M.  F.,  Direction  of  In- 
duced, Rule  for  Deter- 
mining  123,214 

E.  M.  F.,  Effective,  Value  of  239 

E.  M.  F.,  Monocyclic  Dia- 
gram of 271 

E.  M.  F.,  or  Current,  Alter 
nating  Flat-top  Type  of..  235 

E.  M.  F.  of  Self-Induction  . .   127 

E.  M.  F.  of  Voltaic  Cell,  Cal- 
culation of 76,  77 

E.  M.  F.,  Periodic  Alternat- 
ing, Definition  of 233 

E.  M.  F.,  Self-Induced 127 

E.  M.  F.,  Sinusoidal 236 


E.  M.  F.,  Sources  of,  in  Vol- 
taic Cell 67,  68 

E.  M.  F.'S,  Diphase 266 

Earth's  Crust,  Resistance 
of 31,  32 

Earth's  Crust,  Resistivity 
of  Materials  Forming.  . .  30 

Edison-Lalande  Voltaic 
Cell 86,  87 

Efficiency,  Commercial,  of 
Dynamo  Electric  Ma- 
chine  137 

Efficiency  of  Electrical  Dis- 
tribution, Definition  of . .  51 

Efficiency  of  Lamp 207 

Efficiency  of  Lamp,  Effect 
of  Temperature  on 207 

Efficiency  of  Lamp,  So- 
called 207 

Efficiency  of^Lamp,  True. .  207 

Efficiency  of  Voltaic  Bat- 
tery    71 

Electric  Capability  of  Gene- 
rator   131 

Electric  Circuits 57,     64 

Electric  Discharge,  Classi- 
fication of  Effects  of 3 

Electric  Displacement, 
Maintenance  of,  in  Non- 
Conductors  or  Dielectrics  2 

Electric  Displacement, 
Nature  of 2 

Electric  Motor,  Continuous 
Current  Type  of . . .  168  to  192 

Electric  Railroad  Motor.  . .   180 

Electric  Sources     13 

Electric  Sources,  Classifica- 
tion of 14 

Electrical  Effects  . .     . .  i  to      8 


286 


INDEX. 


Electrical  Energy  of  Voltaic 
Cell,  Cost  of 69 

Electrification,  Nature  of . .     10 

Electro-Chemical  Equiva- 
valents,  Tables  of 74 

Electro-Dynamic  Force 
of  Dynamo 170 

Electro-Dynamics  . .  .161  to  168 

Electro-Dynamics,  Defini- 
tion of 161 

Electrolyte,  Action  of  E.M.F. 
on 73 

Electromagnet,  Attractive 
Form  of 119,  120 

Electromagnet,  Portative 
Form  of 118,  119 

Electromagnets 113  to  120 

Electromagnets,  Attractive, 
Definition  of 113 

Electromagnets,  Computa- 
tion of  Attractive  Force 
of 114,  115,  116 

Electromagnets,  Determin- 
ation of  Polarity  of 113 

Electromagnets,  Dual  Char- 
acter of  Flux  in 113 

Electromagnets,  Iron-clad.   119 

Electromagnets,  Induced  or 
Structural  Magnetic  Flux 
of 113 

Electromagnets,  Portative, 
Definition  of ....  113 

Electromagnets,  Prime  or 
Magnetizing  Flux  of 113 

Electromotive  Force  of 
Electric  Sources 14,  15 

Electro-plated  Arc  Carbons  223 

Element  of  Voltaic  Cell 66 

Energy,  Conservation  of  . .       4 

Energy,  Definition  of 3 


Energy,  Doctrine  of  Con- 
servation of 4 

Energy,  Kinetic,  Definition 

of 3 

Energy,  Potential,  Defini- 
tion of 3 

Energy,  Potential,  a  Pos- 
.sible  Variety  of  Kinetic 

Energy 4 

Energy,  Total  Amount  of, 

in  Sun 7 

Entrefer,  Definition  of,  150,  151 
Equivalent,  Electro-Chem- 
ical  74,     75 

Equivalent  Resistance 253 

Erg,  Definition  of 6 

Erg,  Value  of , 6 

Ether,  Stresses  and  Strains 

in i,      2 

Excessive  Heating  of  Dy- 
namo-Electric Machine, 
Limitations  to  Output  of, 
Caused  by 144,  145,  146 

Factor,  Impedance 254,  255 

Feeders. 215 

Ferric  Circuit,  Calculation 

of 108,  109 

Ferric-Magnetic  Circuit 93 

Filament,  Causes  of  De- 
crease of  Cross-Sectional 

Area  of 210 

Filament,  Coking  of 209 

Filament,  Decrease  of  Area 

of  Cross  Section  of 208 

Filament,  Disintegration  of  208 
Filament  of    Incandescent 
Lamp 210 


INDEX. 


287 


Filament  of  Incandescent 
Lamp,  Variation  of,  Dur- 
ing Use, 209 

Film  Cut-out 213,  214 

First  Harmonic,  Frequency 

of 258,  259,  260,  261 

Five-wire  System 61 

Fleming's  Hand  Rule  for 
Direction  of  Induced 

E.  M.  F 123,  124 

Fleming's  Hand  Rule  for 

Motors 163 

Flux  Density,  Definition  of    90 

Flux  Density,  Unit  of 90 

Flux,  Displacement,Nature 

of 2 

Flux    Intensity,  Definition 

of ? 

Flux,  Magnetic 89 

Flux,  Magnetic,  Convention 

as  to  Direction  of 89 

Flux,  Physiologically  Effec- 
tive   206 

Force,  Counter  Electromo- 
tive of  Motor 170 

Force,  Definition  of 3 

Force,  Electric i 

Force,  Electromotive  and 
Electrodynamic,  Co-gen- 
eration of  in  Dynamo  and 

Motor    169 

Force,  Magnetic,  Definition 

of 99,  ioo 

Force  or  Stress,  Electromo- 
tive, Cause  of 2 

Force,  Varieties  of 3 

Formulas  for  Resistivity.22,     23 

Fourier's  Theorem 258 

Frequencies,  Luminous  and 
Non-Luminous.  .,...,.,  201 


Frequencies,  Definition  of.  234 
Frequency    of    First    Har- 
monic  258,  259,  260,  261 

Frequency  of  Second  Har- 
monic  258,  259,  260,  261 

Fuller  Voltaic  Cell 86,     87 

Fuses,  Electric, Capacity  of, 
for  Heat 200 


Galvanometer,  High  Grade 

Thomson's  Mirror. ..  .47,  48 
Galvanometer,  Shunt. .  .36,  37 
Galvanometer,  Thomson's 

Mirror 36 

Gases,  Effect  of  Pressure  on 

Resistivity  of 26 

Gauss,  Definition  of 90 

Generator,  Direct  E.  M.  F.  of  170 
Generator,    Electric    Capa- 
bility of 131 

Generator,  Output  of 130 

Generator,  Series  Wound. .   154 
Generator,  Shunt- Wound ..   154 

Gilbert,  Definition  of 92 

Globes,  Arc-light 231 

Gravity  Voltaic  Cell. . .   84,     85 
Grenet  Voltaic  Cell,. . .  82,     83 

Harmonics 258 

Heat,  Development  of  in 

Safety  Fuse. 200 

Heat,  Dissipation  of,  by 

Electric  Conductor 196 

Heat,  Loss  by  Radiation  . .  197 

Heat,  Radiation  of 197 

Heat,  Unit  of. 192 

Heating,  Electric. . .  .193  to  soo 


288 


INDEX. 


Heating,  Excessive,  of  Dy- 
namo-Electric Machine, 
Limitations  to  Output  of, 

Caused  by 144,  145,  146 

Hefner-Alteneck  Lamp  . . .  205 
High  Resistance    Appara- 
tus, Effect  of  Leakage  on 

Accuracy  of 37 

Hysteresis,  Definition  of. . .   139 
Hysteresis,  Magnetic . .  139, 

140,  141,  142,  143 
Hysteresis,  Magnetic.  Loss 

of  Energy  of 141 

Hysteretic  Diagram 142 

Hysteretic  Loss  in  Alter- 
nating-Current Trans- 
former  276,  277 

Illumination, Physiological, 
Coefficient  of 203 

Illumination,  Physiologic- 
ally Effective 203 

Illuminating  Power,  Phys- 
iologically Effective. .  202,  203 

Impedance  Factor 254,  255 

Impedance  of  Circuit 244 

Incandescent  Lamp,  Activ- 
ity of  7 

Incandescent  Lamp,  Me- 
thods Proposed  for  Re- 
gulating Candle-power 
of 212,  213 

Incandescent  Lighting.. 201 

to  224 

Induced  Electromotive 
Force 121  to  128 

Induced  or  Structural  Mag- 
netic Flux  of  an  Electro- 
magnet   ii 


Inductance,  Influence  of  on 
Sparking  of  Brushes  of 
Dynamo  147,  148 

Induction,  Counter-Electro- 
motive Force  of 62 

Inductor  Alternators   257 

Insulation  Resistance  of 
Line  or  Conductor 33 

Insulator,  Circumstances 
Affecting  Resistance  of. .  33 

Insulator,  Oil 33,     34 

Intake  of  Machine,  Defini- 
tion of 8 

Intensity,  Maximum  of  Arc 
Light ., 221 

Intensity,  Mean  Horizontal, 
of  Arc  Lights 221 

Intensity  of  Flux,  Defini- 
tion of ... 90 

International  c.  G.  s.  Unit 
of  Quantity n 

International  Ohm ,  Defini- 
tion of 17 

International  Practical  Unit 
of  E.  M.  F ii 

Ions,  Definition  of.   73 

Iron-clad  Electromagnets. .   119 

Joint  Admittance 249,  250 

Joint  Resistance 51 

Joule 194 

Joule,  Definition  of 7 

Kinetic  Energy,  Definition 
of 3 

Kirchoff's  Laws 52,     53 

Laborer,  Average  Activity 

of 7 

Lamp,  Carcel 205 


INDEX. 


289 


Lamp,  Effect  of  Tempera- 
ture on  Life  of 207 

Lamp,  Efficiency  of 207 

Lamp    Globe,    Blackening 

of  208,  2ii 

Lamp,  Hefner-Alteneck . . .  205 

Lamp,  Violle 205 

Laws,  Kirchoff's 52,     53 

Lead  of  Dynamo  Brushes..  149 
Leading    Pole    of    Motor- 
Armature  186 

Leakage  Paths.  Magnetic. .     96 
Leakage,  Magnetic,  Effect 
of  on  Efficiency  of  Trans- 
former   277 

Leclanche,  Voltaic  Cell. ...     85 

Lesser  Calorie 192 

Light,  Standard  of 205 

Lighting,  Load  of  Central 

Stations 212 

Limiting  Current  Strength 

in  Wires 198,  199 

Line  or  Conductor,  Insula- 
tion Resistance  of . . .  .33,  34 

Localized  Vector  1 1 

Loop,  Conducting, Rotation 

of,  in  Magnetic  Flux 126 

Losses,  Eddy  Current,  in 
Continuous-Current  Mo- 
tors   174 

Losses,  Magnetic,  in  Dyna- 
mo-Electric Machine,  139,  140 
Losses,  Mechanical,  in  Dy- 
namo-Electric   Machine, 

137,  138,  139 

Luminous  and  Non-Lumin- 
ous Frequencies 201 

Luminous  Radiation, Effect 
of  Temperature  on 204 


M.  M.  F 89,    96 

M.  M   F..  Unit  of .    . .     92 

Machine,  Definition  of  In- 
take of 8 

Machine,  Definition  of  Out- 
put of 8 

Machine,  Dynamo-Electric, 

Commercial-Efficiency  of  137 
Machine,  Dynamo  Electric, 
Principles  UnderlyingDe- 

signof 133,  134,  135 

Machine,  Efficiency  of 8 

Magnetic  and  Material 
Fluxes,  Difference  be- 
tween   91 

Magnetic  Circuits 92 

Magnetic  Conductivity 95 

Magnetic  Force,  Definition 

of  99,  100 

Magnetic  Flux. . . .  89,  104,  112 
Magnetic  Leakage,   Effect 
on   Efficiency  of    Trans- 
former  277 

Magnetic  Losses  of  Dyna- 
mo-Electric Machine  139,  140 
Magnetic  Permeability ....     95 
Magnetic  Reluctance  96  to  104 
Magnetic  Reluctance,  and 
Magnetizing  Force,  Rela- 
tion between 101,  102 

Magnetic  Saturation 92 

Magnetism  Residual 93 

Magneto-Dynamics,  Defini- 
tion of 161 

Magnetomotive  Force 91 

Magnetomotive      Force, 

Structural 93 

Mangin  Reflector. . . . .  .230,  231 

Maximum  Intensity  of  Arc 
Light 221 


2go 


INDEX. 


Mean  Horizontal  Intensity 

of  Arc  Lights 221 

Mean  Spherical  Can  die- 
Power  of  Arc  Lights 221 

Megadyne ,      Approximate 

Value  of 6 

Megadyne,  Definition  of . . .       6 

Megohm,  Definition  of 18 

Megohm,  Standard 30 

Metal-Coated    Arc     Light 

Carbons 223 

Metallic  Reluctivity 103 

Mho,  Definition  of 25 

Microhm,  Definition  of  ...     18 
Molecules,  Dis-associated. .     73 
Molten-Platinum  Standard  205 
Monocyclic  E.   M.    F.,   Dia- 
gram of 271 

Monocyclic  System 271 

Monocyclic  System  Trans- 
former   272 

Motion,  Simple-Harmonic..  236 
Motor- Armature,    Leading 

Pole  of 186 

Motor- Armature,  Reaction 

of 186,  187 

Motor-Armature,   Toothed 

Core  185 

Motor- Armature,    Trailing 

Pole  of 1 86 

Motor-Armatures,    Smooth 

Core.  185 

Motor,  Continuous-Current, 
Speed  Varied  by  Shifting 
Brushes  on  Commutator 

128,  177 

Motor,  Continuous-Current, 
under  Constant  Torque, 
Methods  of  Carrying 
Speed  of... 177,  178,  179 


Motor,  Counter-Electromo- 
tive Force  of 170 

Motor,  Electromotive  Force 

of 62 

Motor,  How  to  Reverse  Di- 
rection of. .  .187,  188,  189,  190 
Motor,  Relation  of  Torque 
and  Speed  to  Activity  of  171 

Motor,  Series 179 

Motor,  Shunt    180 

Motor,  Starting  Resistance 

of 181 

Motor,  Street-car 191 

Motor,  Torque  of 167 

Motor,  Work  Absorbed  by,  170 
Motors,    Classification      of 
for    Torque    and    Speed 

of 171 

Motors,Continuous-Current, 

Eddy  Current  Losses  in..  174 
Motors,     Electric,    Weight 

of 190,  191 

Multiphase  Alternators 265 

Multiphaser 265 

Multiple  Arc  Lighting, 

Cost 227,  228 

Multiple  Circuit 59 

Multiple-Series  Circuit ....     60 
Multiplying     Power     of 
Shunt 36,  37 

Negative  Arc  Light  Carbon, 
Nipple  on 219 

Negative  Charge 2 

Negative  Plate  of  Voltaic 
Cell 66 

Negative  Pole  of  Voltaic 
Cell 66 

Negative  Resistivity  Tem- 
perature Coefficient 23 


INDEX. 


291 


Negative  Terminal  of  Vol- 
taic Cell 66 

Network  of  Conductors, 
Application  of  Ohm's 
Law  to .  53 

Nipple  on  Negative  Arc 
Light  Carbon  219 

Non-Luminous  Radiation..  201 

Obscure  Radiation 201 

Oersted,  Definition  of.         .97 
Ohm,    International,    Defi- 
nition of 17 

Ohm,  Multiples  and  Sub- 
Multiples  of 17.  18 

Ohm,  Standard  .......  29,     30 

Ohrn's  Law  ...         ...49  to     56 

Ohm's  Law,  Application  of, 

to  Branch  Circuit 52 

Ohm's  Law,  Application  of, 
to  Network  of  Conduc- 
tors   53 

Oil  Insulator 33,     34 

Output  of  Dynamo  Electric 
Machine,  Classification  of 

Limitations  to 145 

Output  of  Dynamos  and 
Motors,  Difference  be- 
tween   181,  182 

Output  of  Generator 130 

Output  of  Machine 8 

Parallel  Connection  of  Al- 
ternators   263 

Partz  Gravity  Voltaic  Cell 

85,     86 
Paths,  Magnetic  Leakage. .     96 

Period,  Definition  of 234 

Periodic  Alternating  Cur- 
rent, Definition  of 233 


Periodic- Alternating  E.M.F., 
Definition  of 233 

Periodic  Alternating  E.M.F., 
or  Current.  Peaked  Type 
of 235 

Periodic- Alternating  E.  M.  F.  , 
or  Current,  Sinusoidal 
Type  of.  235 

Permanent  Magnetomotive 
Force 91 

Permeability,  Magnetic ...     95 

Phase 238 

Phase  Detectors 264 

Physiological  Coefficient  of 
Illumination 203 

Physiologically  Effective 
Flux 206 

Physiologically  Effective 
Illuminating  Power.  202,  203 

Physiologically  Eilective 
Illumination 203 

Plate,  Negative,  of  Voltaic 
Cell 66 

Plate,  Positive,  of  Voltaic 
Cell 66 

Poggendorff  Voltaic  Cell  82 ,     83 

Polarity,  Nature  of 2 

Polarization,  c.  E.  M.  F.  of..     8r 

Polarization,  Counter-Elec- 
tromotive Force  of 62 

Pole,  Leading  of  Motor- 
Armature  1 86 

Pole,  Negative,  of  Voltaic 
Cell 66 

Pole,  Positive,  of  Voltaic 
Cell 66 

Pole,  Trailing  of  Motor- 
Armature 186 

Portative  Electromagnets, 
Definition  of 113 


292 


INDEX. 


Positive    Carbon,    Rate  of 

Consumption,  of 228 

Positive  Charge 2 

Positive    Plate   of   Voltaic 

Cell... 66 

Positive  Pole  of  Voltaic  Cell    66 
Positive  Terminal  of  Voltaic 

Cell 66 

Potential  Difference 13 

Potential,  Distribution  of, 
in  Continuous-Arc  Light 

Circuits 226 

Potential     Energy,    Difini- 

tion  of 3 

Power  Factor  of  Alternat- 
ing Current  Transform- 
ers    280 

Practical  Unit  of  E.  M.  F.  . .     u 
Practical   Unit  of  Electric 

Resistance 17 

Practical  Unit  of  Heat. . . .  194 
Projectors  for  Arc  Lights. . 

229,  230,  231 

Quantity,    Electric,     Com 

mercial  Unit  of 45 

Quegohm,  Definition  of 18 

Radiation,  Non  luminous..  201 

Radiation,  Obscure 201 

Radiation  of  Heat 197 

Radiation,  Physiologically 
Effective  Luminous,  Var- 
iation of,  with  Current 

Strength  211 

Radiation,  Standard,  of 
Physiologically  Effective 

Luminous 205 

Railroad  Electric  Motor. . .   180 


Ratio  of  Transformation  . . 

273.  274 

Reactance  of  Circuit 244 

Reflector,  Mangin. ...  230,  231 
Regulation  of  the  Dynamo 

153.  i 60 

Reichsanstalt  Unit 205 

Reluctance,  Magnetic,^  to  104 
Reluctance,  Magnetic,  Defi- 
nition of 97 

Reluctance,  Unit  of 97 

Reluctivity 97 

Reluctivity,  Curves  of,  in 
Iron  and  Steel,  in  Rela- 
tion to  Flux  Density 107 

Reluctivity,  Curves  of,  in 
Iron  and  Steel,  in  Rela- 
tion to  Magnetizing  Force  102 

Reluctivity,  Metallic 103 

Residual  Magnetism 93 

Resistance,  Balances.  ..28,     29 

Resistance,  Electric 17,    40 

Resistance,  Electric,  Nature 

of  Unknown 36 

Resistance,  Equivalent 253 

Resistance,    Insulation    of 

Cable 35,     3& 

Resistance,  Joint 51 

Resistance  of  Insulator, 
Circumstances  Affecting,  33 

Resistance,  Specific 18 

Resistance,  Specific,  Mag- 
netic   97 

Resistance,  Starting  of  Mo- 
tor   181 

Resistance,  Surface  Contact    39 
Resistances,    Formula    for 

Calculating 25 

Resistances,  Methods  of 
Measurement  of ...  .26  to  31 


INDEX. 


293 


Resistivities,   Diagram  of, 

atDifferentTemperatures  21 
Resistivities,  Table  of .  .19,  20 
Resistivities,  Thermal, 

Table  of. 196 

Resistivity 18 

Resistivity,  Formulae 22 

Resistivity,      Temperature 

Coefficients  19 

Reversibility  of  Continuous- 
Current  Dynamo. ..  .170,  171 

Resistivity,  Thermal 194 

Resonant  Circuit 248 

S.  H.  M 236 

Safety  Fuse,  Development 

of  Heat  in 200 

Saturation,  Magnetic 92 

Search  Lights 229 

Second-Harmonic,      F  r  e  - 
quency  of. . .  258,  259,  260,  261 

Self. Induced  E.  M.  F 127 

Semi- Period  of  Alternating 
E.  M.  F.  or  Current  Wave, 

Definition  of 234 

Series  Arc  Light  Circuits . . 

225,  226,  227 

Series  Circuit 58 

Series-Connected    In- 
candescent      Electric 

Lamps 213,  214 

Series  Motor 179 

Series  Motor,  Commutation 

of  Field  Coils  of 179 

Series    Motor,    Method    of 

Varying  Speed  of 179 

Series-Wound  Machine 

187,   188 


Shunt,  Alternating-Current 
Circuit,  MultiplyingPower 

of    252 

Shunt  Circuit,  Application 

of  Ohm's  Law  to 52 

Shunt,  Continuous  Current 
Circuit,  Multiplying 

Power  of 251 

Shunt  Galvanometer 36,     37 

Shunt  Motor 180 

Shunt  Motor,  Care  Re- 
quired in  Starting 181 

Shunt,   Multiplying  Power 

of 36,  37,  251 

Shunt- Wound  Machines, 
Direction  of  Rotation  as 
Motors  and  Generators. . 

187,  188 
Silver  Chloride  Voltaic  Cell 

87,     88 

Simple-Harmonic  Curve. . .  237 
Simple-Harmonic  Motion .     236 

Simple-Periodic  Curve 237 

Single-Fluid  Cells,  Defini- 
tion of 81 

Sinusoidal  Current 236 

Sinusoidal  Current  Circuit, 

Activity  of 253 

Sinusoidal  Curve 237 

Sinusoidal  E.  M.  F 236 

Smee  Voltaic  Cell 82 

Smooth  Core  Motor  Arma- 
tures    185 

Sources,  Electric 13 

Sources,  Electric,  Classifi- 
cation of 14 

Sources,  Electric,  Electro- 
motive Force  of 14,  15 

Sparking  at  Dynamo  Brush- 
es, Cause  of 147,  148 


294 


INDEX. 


Specific  Magnetic  Resis- 
tance   97 

Specific  Resistance,  Defini- 
tion of  18 

Speed  and  Torque,  Classi- 
fication of,  in  Motors. ...   171 
Speed  of  Motor,  Varied  by 
Inserting    Resistance    in 
Armature  Circuit. . .  .177,  178 
Speed  of  Motor,  Varied  by 
Varying  Magneto-motive 
Force  of  Field  Magnets. . 

178,  179 

Standard  Candle 205 

Standard  Cell,  Clark.  ..15,     16 

Standard  Megohm    30 

Standard  of  Physiologically 
Effective  Luminous  Radi 

ation 205 

Standard  Resistance  —  29,     30 
Star      Triphase    Winding, 

Diagram  of     267 

Star- Winding  of  Triphase 

Generator 267 

Step-Down  Transformer.   .  273 

Step-Up  Transformer 273 

Strain,  Displacement   ...9,     10 

Street-Car  Motors 191 

Stress,  Electromotive,  Cause 
of 2 

Stresses  and  Strains  in 
Ether i,  2 

Structural  Magnetomotive 
Force 93 

Sun,  Total  Amount  of 
Energy  in 7 

Surface,  Contact  Resis- 
tance    39 


Table  of  Electro-Chemical 
Equivalents 74 

Table  of  Resistivities — 19,     20 

Table  of  Thermal  Resis- 
tivities   196 

Temperature  Coefficients 
for  Clark  Standard  Cell. .  16 

Temperature  Coefficients 
for  Resistivity 19,  20 

Temperature,  Effect  of,  on 
Efficiency  of  Lamp 207 

Temperature,  Effect  of,  on 
Life  of  Lamp 207 

Temperature,  Effect  of,  on 
Luminous  Radiation. . . .  204 

Temperature,  Effect  of,  on 
Resistivity  of  Conductors  26 

Temperature,  Safe  Limit- 
ing, of  Wire 198,  199 

Terminal,  Negative ,  o  f 
Voltaic  Cell 66 

Terminal,  Positive,  of 
Voltaic  Cell 66 

Thales i 

Therm 192 

Therm-Calorie... 193 

Thermal  Conductivity 194 

Thermal  Resistivities, 
Table  of 196 

Thermal  Resistivity. . .  194,  195 

Thomson's  High  Grade 
Mirror  Galvanometer. 47,  48 

Thomson's  Marine  Galvano- 
meter   46 

Thomson's  Mirror  Galvano- 
meter   46 

Three-Wire  System,  Cal- 
culation of  Current 
Strength  in 55,  56 


INDEX 


295 


Three  Wire  System,  De- 
scription of 54,  55 

Three- Wire  System, Neutral 
Wire  in  55 

Toothed  Core  Motor- Arma- 
ture   185 

Torque  and  Speed,  Classifi- 
cation of,  in  Motors..  171 

Torque  and  Speed,  Rela- 
tion of,  to  Activity  of 
Motor  .  . . 171 

Torque  of  Motor 167 

Trailing  Pole  of  Motor- 
Armature. 186 

Transformation,  Ratio  of 

273.  274 

Transformer,  Step-Down. .  273 

Transformer,  Step-Up 273 

Transient  Magnetomotive 
Force 91 

Tregohm,  Definition  of  ..       18 

Triangular  Triphase  Wind- 
ing Diagram  of 267 

Triangular  Winding  of  Tri- 
phase Generator 267 

Tricrohm,  Definition  of....     18 

Triphase  Circuit,  Analysis 
of 270 

Triphase  E.  M.  F'S 267 

Triphase  E.  M.  F.'S,  Diagram 
of 268 

Triphase  Generator,  Star- 
Winding  of 267 

Triphase  Generator,  Wind- 
ing of 267 

Triphase  Generators,  Tri- 
angular-Winding of 267 

Unit  Arc-Light  Crater  In- 
tensity   223 


Unit  of  Activity,  c.  G.  s 7 

Unit  of  Flux,  Density  of  . .  90 

Unit  of  Force,  c.  G.  s 5 

Unit  of  Heat 192 

Unit  of  Illumination,  Name 

Proposed  for 206 

Unit  of  M.  M.  F 92 

Unit  of  Quantity,  c.  G.  s. . .  n 

Unit  of  Reluctance 97 

Unit  of   Resistance,  Prac- 
tical, Definition  of 17 

Unit  of  Work 6 

Units,  c.  G.  s 4,  5 

Units,    Fundamental,    Sci- 
entific  4,  5 

Vector,  Localized 1 1 

Vector  Quantities 1 1 

Violle  Lamp 205 

Virtual      Counter-Electro- 
Motive  Force 62 

Voltaic  Cell 65  to  88 

Voltaic  Cell,  Calculation  of 

E.  M.  F.  in 76,  77 

Voltaic  Cell,  Cost  of  Elec- 
tric Energy,  produced  by  69 
Voltaic  Cell,  Elements  of . .  66 
Voltaic  Cell,  Simple  Form 

of 67 

Voltaic    Cell,     Source     of 

E.  M.  F.  of 67,  68 

Voltaic  Cells,  Classification 

of 81 

Voltaic  Couple 66 

Water-Gramme  -Degree- 

Centigrade 193 

Water,  Pure,  Resistivity  of  21 

Wave,  Complex-Sinusoidal  258 

Wheatstone's  Balance  .  28,  29 


296 


INDEX. 


Wheatstone's  Bridge,  Vari- 
ous Forms  of 28,  29 

Winding,  Combination  Tri- 
phase  . .  268 

Wire,  Formula  for  Calcula- 
ting Size  of,  Required  to 
Fill  Given  Bobbin. 37,  38,  39 


Wires ,  Limiting  Current 
Strength  in 198,  199 

-Work,  Absorbed  by  Mo- 
tor   170 

Work,  Definition  of 3 

Work  Unit  of...  6 


ERRATA. 

Page  23,  If  23,  5  lines  from  bottom  of  page.    For  resistivity  of  a  mile 

read  resistance  of  a  mile.  ^ 
"    24,  Syllabus,  9th  line.     For  begohm  read  bicrohm.   - 


34,  1[  34.     For  R  = 


rapp.  coth-i  \/  ^      <, 

-ttapp. 

read  R  =  \/R&pv.  rapp.  /tanbr  ' 


34,  last  line.     For  coth 


V; 


2656 


read  1  /  tanh 


-iA/2656 

V     R(Y).A 


6024  "  K    6024 

"  175,  If  182.     For  reluctance  read  retardation.    ~* 
"  203,  "  211.     For  yellow  read  green.    -S 
"  230,  Fig.  77,  caption.     For  Magnetic  read  Mangin. 
44  258,  If  261.     For  n—\  read  n  +  1.  - 
"  264,  Syllabus.     For  n— 1  read  n  +  1.    J 


OT  THB 

UJIVEBSITT 


ill 


